A finding of any one of the grounds separately enumerated under Section 7A-289.32 is sufficient to support termination of parental rights. In re Tyson, 76 N.C. App. 411, 415, 333 S.E. 2d 554, 557 (1985). However, DSS has the burden to prove all the facts justifying the termination ground asserted by clear, cogent, and convincing evidence. N.C.G.S. Sec. 289.30(d)-(e) (1981) (court must adjudicate existence or nonexistence of “any of the circumstances” authorizing termination; petitioner must prove facts by clear, cogent and convincing evidence); compare N.C.G.S. Sec. *1837A-289.32(3a) (1986) (burden on petitioner to prove facts justifying termination by “clear and convincing” evidence) with In re Montgomery, 311 N.C. 101, 109, 316 S.E. 2d 246, 252 (1984) (“clear and convincing” and “clear, cogent and convincing” describe same evi-dentiary standard).
The instant case therefore presents two issues: (I) Under Section 7A-289.32(3), whether there was clear, cogent and convincing evidence that either Evans or Ryals had (A) “willfully” left his child in foster care for more than two consecutive years without showing either (B) “substantial progress” in correcting the conditions leading to the child’s removal or (C) “positive response” to the “diligent efforts” of DSS; and (II) under Section 7A-289.32(6), whether there was clear, cogent and convincing evidence that “prior to the filing of the termination petition,” neither respondent had established paternity, legitimated his child or otherwise provided support or care under the statute.
I
A
In order to terminate parental rights under the applicable pre-1985 version of Section 7A-289.32(3), petitioner must prove (a) the parent has “willfully left the child in foster care for more than two consecutive years” without showing (b) “substantial progress” in correcting those conditions that led to the child’s removal or (c) “positive response” to the “diligent efforts” of DSS to encourage the parent to strengthen the parental relationship or plan for the child’s future. See In re Wilkerson, 57 N.C. App. 63, 68-69, 291 S.E. 2d 182, 184-85 (1982) (upholding termination where evidence established all three requirements); In re Tate, 67 N.C. App. 89, 92-94, 312 S.E. 2d 535, 538-39 (1984) (upholding separate findings of lack of substantial progress and positive response).
As to the respondents’ “willfully” leaving their respective children in foster care, the trial court found both respondents “have evidenced a settled purpose and willful intent to forego all parental duties and obligations and to relinquish all parental claims to their respective children in this matter.” Although Section 7A-289.32(3) merely requires proving the parents willfully left their child in foster care for two years, we note the court’s finding restates the common definition of the broader concept of *184“abandonment.” E.g., In re Maynor, 38 N.C. App. 724, 726, 248 S.E. 2d 875, 876-77 (1978). Although petitioner alleged “willful abandonment” as a ground for termination, the court did not terminate respondents’ rights on the specific ground of abandonment or neglect. Cf. In re Smith, 56 N.C. App. 142, 147, 287 S.E. 2d 440, 443, cert. denied, 306 N.C. 385, 294 S.E. 2d 212 (1982) (“abandonment” under N.C.G.S. Sec. 7A-517(21) (1981) supports termination for “neglect” under N.C.G.S. Sec. 7A-289.32(2) (1981)); see also N.C.G.S. Sec. 7A-289.32(8) (1986) (adding “willful abandonment” for six months prior to petition as ground for termination). Although the breadth of “willful abandonment” should often encompass “willfully leaving” a child in foster care, the broad finding of willful abandonment is not essential to the more limited determination required under Section 7A-289.32(3).
[1] While their brief is not altogether clear on this point, respondents apparently contend that their periodic incarcerations could preclude finding either respondent “willfully” left his child in foster care for two consecutive years. However, a respondent’s incarceration, standing alone, neither precludes nor requires finding the respondent willfully left a child in foster care. Compare In re Burney, 57 N.C. App. 203, 206, 291 S.E. 2d 177, 179 (1982) (rejecting argument that periods of incarceration preclude such finding) with Maynor, 38 N.C. App. at 726-27, 248 S.E. 2d at 877 (1978) (incarceration alone is insufficient to show willful abandonment). Although he was apparently not incarcerated during the entire two-year period being considered, we note Evans has never attempted to contact DSS or his child during that period. Ryals has been incarcerated throughout the period; he has similarly never contacted DSS, but did call his child once at her foster home in May 1985. In accord with our decision in Burney, we think these facts demonstrate respondents’ leaving their children in foster care was “willful.” Burney, 57 N.C. App. at 206, 291 S.E. 2d at 179.
B
[2] Petitioner neither alleged nor did the trial court find that respondents had failed to show substantial progress in correcting the conditions leading to the removal of their children. The trial court apparently misconstrued Section 7A-289.32(3) to allow termination where petitioner could show either respondents’ lack of *185substantial progress or respondents’ lack of positive response. A careful reading of the statute reveals Section 7A-289.32(3) requires the petitioner to prove that the parent has not shown either substantial progress or positive response; thus, petitioner must prove the absence of both substantial progress and positive response in order to justify terminating respondents’ parental rights under subsection (3). Cf. Tate, 67 N.C. App. at 92-94, 312 S.E. 2d at 538-39; Wilkerson, 57 N.C. App. at 68-69, 291 S.E. 2d at 184-85; N.C.G.S. Sec. 7A-289.30(d) (1981) (court shall adjudicate existence or nonexistence of “any of the circumstances” authorizing termination under Section 7A-289.32); see also Burney, 57 N.C. App. at 206, 291 S.E. 2d at 179 (although discussion limited to affirming finding that respondent lacked “positive response,” court noted other findings established respondents’ failure to make “substantial progress”).
Accordingly, we conclude the court could not terminate respondents’ parental rights under Section 7A-289.32(3) absent the necessary additional conclusion and supporting findings that respondents failed to show substantial progress in correcting the conditions leading to the removal of their children.
C
[3] Even had the court found that respondents failed to make the necessary substantial progress under Section 7A-289.32(3), we also hold the court improperly concluded that both respondents failed to “show positive response to the diligent efforts” of DSS to encourage each respondent to strengthen his respective parental relationship or plan for his child’s future. The court made only one finding directly relevant to this conclusion: noting Evans was “presently” in prison, the court found that DSS unsuccessfully wrote to Evans in Greensboro and that “efforts by [DSS] to contact . . . Evans have been futile . . . .” There is simply no finding showing any DSS attempt to provide services or counsel to Ryals, or even showing any DSS attempt to locate him: the court only noted that Ryals did not contact DSS after DSS acquired custody of his child. Regardless of any evidence supporting these findings, the findings are themselves legally insufficient to discharge DSS’s burden to show, with clear and convincing evidence, its diligent efforts to encourage respondents to strengthen their parental relationships or undertake planning for their children’s future. Cf. *186 Wilkerson, 57 N.C. App. at 69, 291 S.E. 2d at 185 (summarizing respondents’ lack of positive response to petitioner’s diligent efforts which included 6V2 years of continuous contact, frequent home visits and counselling attempts); Tate, 67 N.C. App. at 93, 312 S.E. 2d at 538-39 (petitioner referred respondent for alcoholism and employment services, assisted securing and maintaining housing, kept abreast of respondent’s progress and stayed in touch with other agencies).
We recognize both respondents were incarcerated during part or all of the two-year period under consideration. We note the court did specifically find that “efforts to contact” Evans had been “futile.” Assuming arguendo that this finding supports the court’s conclusion that respondents did not show positive response to DSS’s diligent efforts, the finding is not itself supported by competent evidence. The only evidence pertaining to this finding is the case worker’s testimony that she sent a letter to Greensboro inviting Evans to a DSS review. The case worker took no further action after the letter was returned. This evidence does not constitute clear and convincing proof that efforts to contact Evans were futile.
In any event, DSS’s lone attempt merely to contact Evans hardly approaches the diligent efforts to strengthen family ties approved in Wilkerson and Tate. Other than the letter to Evans, we find no evidence in the record of any attempt even to contact either respondent other than the DSS affidavit for service by publication under N.C.G.S. Sec. 7A-289.27 (1981). This affidavit may evidence the “due diligence” necessary for service under that statute. See generally In re Clarke, 76 N.C. App. 83, 85-87, 332 S.E. 2d 196, 198-200, disc. rev. denied, 314 N.C. 665, 335 S.E. 2d 322 (1985). However, petitioner’s “due diligence” in serving its petition after 29 December 1983 does not determine whether it made “diligent efforts” to encourage and counsel family relationships for two consecutive years prior to termination under Section 7A-289.32(3).
Although the court made no findings concerning Ryals on this issue, we note the revealing testimony given by the case worker: “I’ve never offered . . . Ryals a service contract to sign. He has been in jail and it would not make sense to provide him with a service contract .... To my knowledge no one has taken *187the children out to where . . . Ryals is in jail.” As to DSS’s “diligent efforts,” we hold only that DSS has shown no diligent efforts whatsoever to help respondents; however, we are cognizant Section 7A-289.32(3) must on occasion be applied to a respondent who has been incarcerated during part or all of the two-year (now eighteen-month) trial period. Like DSS, future petitioners may conclude any attempt to contact an incarcerated respondent is “futile.” Whether or not such an assessment is reasonable, the respondent’s obligation to respond positively to DSS’s diligent efforts certainly presupposes some stimulus from DSS. Thus, we question whether a court may conclude a respondent failed to respond positively to DSS’s allegedly “diligent efforts” under Section 7A-289.32(3) where DSS never actually made contact with respondent in any way. Cf. Maynor, 38 N.C. App. at 727-28, 248 S.E. 2d at 877-78 (since abandonment under N.C.G.S. Sec. 48-2(3b) (1976) requires proof of DSS “diligent efforts,” insufficient evidence to find abandonment where no DSS contact with respondent).
Respondents also except to the court’s finding that they have evidenced a “settled purpose” to relinquish all parental claims to their respective children. Since the court did not terminate respondents’ rights for “neglect” under Section 7A-289.32(2), we do not pass on the sufficiency of evidence supporting the court’s finding that respondents had, in effect, willfully abandoned their children. However, assuming clear and convincing evidence supports this finding, the court might properly consider terminating respondents’ rights for “neglect” under Section 7A-289.32(2). See Smith, 56 N.C. App. at 147, 287 S.E. 2d at 443; see also In re Graham, 63 N.C. App. 146, 150-51, 303 S.E. 2d 624, 627, cert. denied, 309 N.C. 320, 307 S.E. 2d 170 (1983) (incarcerated respondent’s lack of involvement with child established neglect under Section 7A-289.32(2)).
II
{4] The court also concluded neither respondent had “established paternity of [his] respective child . . . judicially or by affidavit” prior to the filing of the petition on 29 December 1983; the findings supporting this legal conclusion merely restate it. We must reverse the court’s legal conclusion on two grounds. First, the record only reveals evidence of the respondents’ paternity as *188of one month before the petition was filed. Section 7A-289.32(6) requires that petitioner show respondents have failed to comply with its terms “prior to the filing of a petition to terminate . . . parental rights”: Either respondent could have established his paternity or the legitimacy of his child during that one-month period. Since the only logical construction of subsection (6) under Montgomery is that DSS carries the burden to prove the lack of paternity or legitimacy as of the petition’s filing date, we hold DSS failed to discharge the admittedly difficult evidentiary burden of proving the absence of a fact. See Montgomery, 311 N.C. at 109-10, 316 S.E. 2d at 252.
In addition, the court made no findings on the other three circumstances under Section 7A-289.32(6) by which respondents could legitimize their children or show substantial support or care. As with the similarly-phrased provisions of Section 7A-289.32(3), the language of Section 7A-289.32(6) dictates that DSS must prove respondents failed to take, not one, but any of the four actions listed in parts (a)-(d) of Section 7A-289.32(6). See Tyson, 76 N.C. App. at 416, 333 S.E. 2d at 537 (termination under subsection (6) authorized where court found respondent “never established paternity, legitimated the child, or provided substantial support or care”). While we note a county attorney alleged the respondents’ “putative” fatherhood in the DSS affidavit for publication, we reject the contention that the allegation constitutes clear, cogent and convincing evidence that respondents failed to comply with Section 7A-289.32(6). Indeed, the record reveals Ryals provided significant financial support before his incarceration. While his support was less substantial, Evans also provided some funds during his incarceration. Thus, if respondents’ parental rights are to be terminated under Section 7A-289.32(6), there must be further fact-finding to determine all the circumstances under parts (a)-(d) of the section.
Ill
As the trial court’s findings are insufficient to terminate respondents’ parental rights upon the grounds cited, we vacate the trial court’s order terminating respondents’ rights and remand the case for further proceedings not inconsistent with this opinion.
*189Vacated and remanded.
Judge COZORT concurs.
Judge Phillips concurs in the result.