Each side in the abortion battle made inroads in the other's bastions in Tuesday's elections, setting the stage for a new round of struggles when state legislatures convene next year.

Abortion opponents are preparing to push for tough new restrictions in Michigan and Ohio, where voters replaced governors who supported abortion rights with chief executives opposed to abortion. But the National Abortion Rights Action League (NARAL) pointed to victories of abortion-rights candidates in gubernatorial contests in Florida and Texas, two states where antiabortion forces have showed strength.

What was clear amid the claims and counterclaims was that the 1990 elections did not turn into the great national abortion referendum that some anticipated a year ago. Instead, abortion took its place behind such issues as the deficit, education and the environment and was a decisive factor for only a committed minority.

Exit polls suggested that this helped abortion's opponents more than supporters of abortion rights. Abortion foes were twice as likely as abortion-rights supporters to say that abortion had been one of the two issues that determined how they voted.

A nationwide poll of 9,444 voters conducted by Voter Research and Surveys for a consortium of news organizations found that among all voters, only 14 percent thought abortion should be illegal in all circumstances. But among voters who said abortion had been a voting issue for them, 32 percent said abortion should be illegal.

Roughly 40 percent of each group thought abortion should be legal in all circumstances.

In House races, the abortion issue appeared to have helped Republicans slightly more than Democrats. GOP House candidates ran about 5 percentage points better among voters who made abortion a voting issue.

Abortion-rights supporters gained eight seats in the House and two in the Senate, but Douglas Johnson, the legislative director for the National Right to Life Committee, said abortion opponents still have a big enough margin to sustain a presidential veto of abortion-rights legislation.

Most of next year's battles, however, will be in the states, and exit polls showed the vast difference in the terrain. In California and Oregon, for example, more than half the voters believe abortion should be legal in all circumstances. But in Kentucky and South Dakota, fewer than 20 percent of the voters felt this way.

In the battle for legislatures, both sides agreed that abortion-rights supporters now have majorities in the Idaho Senate and the Montana House, while abortion foes took over the North Dakota Senate and the West Virginia House. Abortion-rights forces said they had strengthened their hand in the Arizona House and Senate and the Florida House. Abortion foes made the same claim for the New York Senate and both houses in Ohio.

Antiabortion forces pointed to the defeat of several politicians who had switched from an antiabortion to an abortion-rights position at the start of their campaigns. These included Kansas Gov. Mike Hayden (R), upset by abortion foe Joan Finney (D); Anthony Celebrezze (D), who lost his gubernatorial bid in Ohio to abortion opponent George Voinovich (R); and Paul Hubbert (D), who lost to Alabama Gov. Guy Hunt (R).

And abortion opponents beat back efforts to unseat a number of their most prominent lawmakers. In Pennsylvania, the most visible antiabortion activist in the state legislature, Stephen F. Freind, a Havertown Republican, survived even though he was targeted by NARAL. And in Wisconsin, the Senate majority leader, abortion-rights supporter Joseph Strohl, a Democrat from Racine, was unseated by an abortion foe, Republican George Petak.

But abortion-rights supporters also had their victories. In California, Kurt Pringle, a Republican state assemblyman whose antiabortion efforts earned him a spot as one of the top nine in the nation marked for defeat by NARAL, lost his Orange County seat to Democrat Tom Umberg. And in Pennsylvania, an antiabortion leader in the Senate, M. Joseph Rocks, a Republican, lost his Philadelphia district seat to a longtime abortion-rights activist, Democrat Allyson Schwartz.

Abortion-rights activists claimed a major victory in Idaho, where the legislature passed a restrictive abortion bill last year that was vetoed by Gov. Cecil D. Andrus (D). Andrus easily won reelection and abortion-rights supporters say they have a commanding majority in the state Senate that will stop any new antiabortion legislation in the 1991 session.

Among the defeated legislators was state Sen. Roger Madson (R), the sponsor of last session's restrictive abortion bill, who lost to abortion-rights advocate Cynthia Scanlon.

Abortion-rights forces also could claim victory in the only three statewide referenda on the issue. Voters in Oregon turned down two proposals, one that would have banned most abortions and one that would have required parental notification before a minor could get an abortion. In Nevada, voters kept a 17-year-old law on the books that makes abortion legal through the 24th week of pregnancy.

The governor's seat in seven states -- Florida, Georgia, Rhode Island, Texas, California, Minnesota and New Mexico -- passed from an abortion opponent to an abortion-rights supporter, while in four states -- Kansas, Ohio, Alaska, Michigan -- the trend went the other way.

Both sides agreed that Michigan was the most likely early battleground. "It has the potential to be another Pennsylvania," said NARAL spokeswoman Loretta Ucelli. Pennsylvania enacted one of the nation's most restrictive abortion laws last year.

Despite the lack of any clear national mandate on the abortion issue, exit polls suggested that both parties are increasingly identified with particular sides of the issue: Democrats for abortion rights, Republicans against abortion. Among voters who said abortion was a voting issue, 62 percent of self-described Democrats said abortion should be legal under all circumstances. But among Republicans who voted on abortion, only 22 percent took this view.

Polling assistant Sharon Warden contributed to this report.

This chart shows how voters on Election Day responded to the question:

"Which of these statements comes closest to your view about abortion?

1) It should be legal in all circumstances; 2) It should be legal only in

some circumstances; or 3) It should not be legal in any circumstances."

.........................Always..Sometimes..Never

.........................Legal...legal......legal

Alabama.................. 23%...... 57%.....20%

Alaska................... NA...... NA...... NA

Arizona.................. 39...... 44...... 17

Arkansas................ 24...... 54...... 21

California.............. 56...... 33...... 12

Colorado................ 45...... 41...... 14

Connecticut............. 48...... 39...... 13

Delaware................ 44...... 41...... 15

District of Columbia.... 51...... 36...... 13

Florida................. 47...... 41...... 12

Georgia................. 33...... 50...... 17

Hawaii.................. 45...... 42...... 13

Idaho................... NA...... NA...... NA

Illinois................ 40...... 45...... 15

Indiana................. 31...... 49...... 21

Iowa.................... 32...... 51...... 18

Kansas ................. 33...... 50...... 17

Kentucky................ 19...... 55...... 26

Louisiana............... NA...... NA...... NA

Maine................... 48...... 40...... 12

Maryland................ 46...... 41...... 13

Massachusetts........... 45...... 41...... 13

Michigan................ 34...... 48...... 18

Minnesota............... 36...... 47...... 17

Mississippi............. NA...... NA...... NA

Missouri................. NA...... NA...... NA

Montana................. 32...... 50...... 18

Nebraska................ 29...... 47...... 24

Nevada.................. 37...... 49...... 13

New Hampshire........... 45...... 42...... 13

New Jersey.............. 39...... 43...... 18

New Mexico.............. 31...... 48...... 21

New York................ 42...... 43...... 15

North Carolina.......... 30...... 52...... 18

North Dakota............ NA...... NA...... NA

Ohio.................... 37...... 48...... 16

Oklahoma................ 31...... 53...... 17

Oregon.................. 55...... 33...... 12

Pennsylvania............ 32...... 50...... 18

Rhode Island............ 44...... 40...... 16

South Carolina.......... 26...... 56...... 17

South Dakota............ 18...... 53...... 28

Tennessee............... 28...... 52...... 20

Texas................... 33...... 51...... 16

Utah.................... NA...... NA...... NA

Vermont................. 50...... 38...... 12

Virginia................ NA...... NA...... NA

Washington.............. NA...... NA...... NA

West Virginia........... 22...... 54...... 24

Wisconsin............... 28...... 50...... 22

Wyoming................. 27...... 57...... 17

Figures are based on a random sample of voters from each state; absentee voters are not included. Respondents filled out questionnaires anonymously as they left the polls; none was interviewed directly. Where no figures appear, data were not available. Figures may not total 100 percent because of rounding. Margin of sampling error is plus or minus 3 percentage points. The exit poll was designed by Voter Research and Surveys of New York. Interviewing was conducted by Chilton Research Services of Radnor, Pa.