This appeal comes to us from a second order mandating that the parties and infant child undergo blood tests to establish paternity of the child. We dismiss the appeal due to the absence of an appealable order.
On December 4,1991, appellee David Leslie Chilldres filed a Complaint to Establish Paternity in Pulaski County Chancery Court. He alleged that from March 19 to mid-April, 1991, he and the defendant, appellant Patricia Scheland, were actively dating though Mrs. Scheland was married at the time, and that Mrs. Scheland had become pregnant with his child, which was estimated to be due in the January 15, 1992 time frame. Chilldres stated that Mrs. Scheland had acknowledged his paternity to several persons. Chilldres subsequently joined Mrs. Scheland’s husband of nineteen years, Tom Scheland, as a party defendant.
Chilldres sought to be declared the father of the child and requested that he be given visitation rights and allowed to support the child and pay part of the birth expenses. The child was born on January 6, 1992.
In a counterclaim filed on February 3,1992, Mrs. Scheland prayed that in the event that Chilldres’s allegations were proved, she be paid $26,109.92 for prenatal care and laying-in expenses, $5,584 in lost wages, and child support in an amount to be set by the court. She also prayed, irrespective of the paternity determination, that she be awarded $13,282.50 for psychiatric-psychological treatment and damages for future physical pain, suffering, and medical treatment resulting from Chilldres’s mental abuse as well as $100,000 in punitive damages.
Mrs. Scheland filed an answer to Chilldres’s complaint, also on February 3, 1992, denying Chilldres’s allegations and asserting that under the common law the husband of a married woman is presumed to be the father of all children of the married woman and that it would be contrary to public policy to permit Chilldres to interfere with the Schelands’ marital relationship. In an amended answer filed on June 5,1992, the Schelands objected to Chilldres’s efforts “to illegitimize their child that was conceived in wedlock and born in wedlock.”
Following a hearing, the chancellor ordered that blood tests be performed on Chilldres, the Schelands, and the infant child to *167assist in deciding paternity under her authority set out in Ark. Code Ann. § 16-43-901(e) (Supp. 1991). The Schelands then filed a motion to dismiss that order, contending that Chilldres’s admission that the child was conceived and born in wedlock established that the child was not illegitimate as a matter of law and that the Schelands’ constitutional right to marital privacy barred any attempt by Chilldres to illegitimize their child. In his answer, Chilldres declared that the matter had already been decided by the Court in the first order and was therefore res judicata.
In a second order, the chancellor denied the motion to dismiss and reiterated her earlier order requiring the parties and the child to submit to blood tests to assist her in determining paternity. The Schelands filed notice of an interlocutory appeal from the chancellor’s second order. No further orders have been entered by the chancellor. The issue of paternity and the counterclaim by Mrs. Scheland remain to be decided.
Supreme Court Rule 29(1 )(k) permits interlocutory appeals, and Rule 2(a) of the Appellate Rules of Procedure specifies those orders that are appealable. Though the Schelands direct us to Rule 2 and state generally that it provides for an appeal to this court in this case, they fail to premise jurisdiction on a particular subsection of Rule 2 or otherwise to tell us why an interlocutory appeal is appropriate under our rules. None of the categories for interlocutory orders from which appeals may be taken under Rule 2(a) embrace an order for blood tests such as that contemplated in this case. The fact that a significant issue may be involved is not sufficient, in itself, for this court to accept jurisdiction of an interlocutory appeal. An appeal is simply premature at this time. See Stephens v. Stephens, 306 Ark. 59, 810 S.W.2d 946 (1991). We hold that the chancellor’s order is not appealable.
Appeal dismissed.