A bill requiring parental or judicial consent for abortions for unmarried girls under 18 won final approval from the Virginia House on a 78-to-21 vote today and appeared headed for a heated contest in the Senate.

Proponents of the measure, including Del. Clinton P. Miller (D-Shenandoah), described it as an "opportunity for better-educated counseling" for minors.

But Del. Franklin M. Slayton (D-Halifax), one of the measure's foes, asserted: "This is going to be the biggest boon for illegal, back-street abortion clinics this state has had for many years."

A handful of state senators watched the emotional, 30-minute proceedings from the rear of the House chamber. Sen. Charles L. Waddell (D-Loudoun), who said he hadn't decided how he will vote on the measure, predicted it would pass the Senate if it can survive the courts committee that will take it up next.

Sen. Joseph V. Gartlan Jr. (D-Fairfax) said, "I expect it will probably pass. But that is not a prediction."

To a certain extent, legislators attribute the bill's success so far to a growing conservatism and the build-up of pressure from antiabortion forces. Del. Vincent F. Callahan (R-Fairfax) said the same bill would "probably not" have passed five years ago.

Del. Mary A. Marshall (D-Arlington) described the trend as an increasing "fundamentalist, restrictive view of what government can do and the desire to have government intervene in people's private lives."

Del. Robert Harris (R-Fairfax) sees it more positively: "We're trying in this country to strengthen family bonds and bring the family unit closer together. This bill . . . would mean stronger family ties."

The measure, which enjoys a powerful sponsor in Del. Theodore V. Morrison Jr. (D-Newport News), would require unwed, pregnant girls under 18 whose parents have not consented to an abortion to obtain the approval of a juvenile court judge through an expedited court procedure. If the judge finds the minor is mature enough to make up her own mind, the bill says, he should grant the approval. If the judge finds the minor is too immature to make such a choice, he can approve the abortion if he finds it is in the girl's best interest.

The measure won initial approval from the House Sunday night after 1 1/2 hours of emotional debate. Today's final approval was preceded by statements from delegates, but not formal debate. The House gallery was packed with antiabortion activists who quietly filed out of the chamber after the vote.

Similar bills have become a fast-spreading trend in state legislatures since a 1979 Supreme Court decision that laid out the constitutional guidelines for requiring parental notification or consent.

Twelve states have enacted laws requiring clinics to notify parents of a minor's request for an abortion, and nine states have passed laws requiring parental or judicial consent, according to the Planned Parenthood Federation of America. Sixteen of the 21 laws have been enacted since 1980.

Seven statutes were struck down or temporarily enjoined by lower courts for reasons ranging from insufficient protection of a minor's right to confidentiality in a court hearing to a failure to provide for a speedy appeal of a judge's decision.

About 4,000 of the 30,000 abortions done yearly in Virginia are performed on girls under 18, according to Bennet Greenberg, executive director of the Virginia Planned Parenthood Affiliates. Opponents and supporters of Morrison's bill agree that about two-thirds of the minors first consult with their parents before undergoing the procedure.

Opponents such as Marshall argue that the remaining one-third don't go to their parents "for very good reasons. A great many of the very young girls have been victims of incest." To expect them to go to court for approval, argues Del. Warren G. Stambaugh (D-Arlington), "is insane." He predicted the result would be fewer abortions.

Proponents such as Miller argued that minors must seek their parents' consent for even simple operations like tonsillectomies. "Parents," Morrison said during Sunday night's debate, "ought to have some rights too. [This is] as much we can do constitutionally."

Many members decided the issue based on their own experiences raising children. "I have two daughters," said Del. Gladys Keating (D-Fairfax), who voted for the measure today. "The thought of them going through something like that alone is rough."