Republicans scored small but significant legislative gains Nov. 6

Republicans will be more visible and presumably more audible in state legislatures next year. But Democrats will continue to dominate the legislative process in most states for at least another two years, as they have for decades.

Overshadowed by the Nov. 6 reelection of President Ronald Reagan and the picking up of 15 more seats in the US House of Representatives were GOP gains in more than half the state lawmaking chambers, from Maine to Hawaii.

While it is uncertain what impact the increased number of Republican legislators might have in the coming months, some observers view it as contributing to a more conservative mood within state lawmaking circles.

With legislatures in all but a handful of states scheduled to be in session by late January, a variety of issues soon will be vying with budget-shaping for major attention.

Measures to be debated involve containment of health-care costs, restrictions on toxic waste disposal, stiffer drunk driving penalties, curbs on utility rates , mandatory use of auto seat belts, government reorganization, improvement in public schools, and equal pay for comparable jobs.

Although tax proposals are expected to be considerably less prevalent than in most recent years, at least one state will probably see a strong push in that direction. Democratic Speaker-elect Vera Katz of the Oregon House of Representatives is throwing her support behind a limited state sales tax, with receipts committed to lowering property taxes.

Prospects for the controversial proposal could hinge substantially on at least some degree of support that cuts across party lines. Republican Gov. Victor Atiyeh, who in the past opposed a sales tax, apparently will submit his own proposal for such a levy.

Oregon Democrats control both the state Senate and House, although by slightly narrower margins than before the November election. The state is one of 26 where the governorship and at least one chamber of the legislature will be in the hands of different parties.

Despite an overall net gain of 332 legislative seats, Republicans at 1985 lawmaking sessions will be outnumbered 4,344 to 3,057 by Democrats. There are also nine independents, one Libertarian Party member, and 49, the full membership of the Nebraska Senate, are officially ''nonpartisan.''

The GOP will have a majority in both senate and house in 11 states, while the Democrats will be dominant in 27. In nine others one party controls the senate and the other the lower legislative chamber, while in two more states - Montana and New Mexico - one branch is Democratic controlled and the other is evenly divided in membership between the two parties. Nebraska's unicameral legislature is nonpartisan.

Prior to the November election Republicans dominated in both branches of 10 legislatures, Democrats held majorities in 34 states, and only four were under split control.

The biggest political turnaround is in Connecticut, where GOP gains of 11 seats in the 36-member Senate and 23 in the 151-member House shift control in both chambers from the Democratic opposition. Gov. William A. O'Neill, a Democrat, thus faces a 24-to-12 Republican majority in the Senate and a 87-to-64 Republican majority in the House.

Other legislative chambers newly controlled by Republicans are the Ohio Senate and the houses of representatives in Delaware, Minnesota, Nevada, and North Dakota. The GOP also pulled even with the opposition party - at 21 seats apiece - in the formerly Democratic-controlled New Mexico Senate.

Numerically, the largest single Republican increase came in the 400-seat New Hampshire House, where a gain of 58 Republicans increases the party's majority to 296 to 103, with one vacancy. The GOP also increased its control in the Granite State's 24-member Senate from a 15- to 18-seat majority. GOP Gov. John Sununu also won a second two-year term.

In Idaho the GOP increased its legislative majority by 23 seats - seven in the Senate and 16 in the House, thus making it possible to override, along purely party lines, a veto by Democratic Gov. John V. Evans.

North Carolina Democrats retained control of both lawmaking chambers, but in the process Republicans picked up seats - six in the Senate and 19 in the House - and won the governorship.

Another particularly significant potential increase in GOP legislative clout occurred in Nevada, where an overall 10-seat gain, including six in the formerly Democratic-controlled 42-member House now gives Republicans 25 to 17 majority. Despite four more GOP Senate seats, however, that chamber remains in Democratic hands. Gov. Richard H. Bryan, now halfway through his four-year term, is a Democrat.

A net increase of 13 Republicans in the Minnesota House has shifted control of that chamber to the GOP, with a 70 to 64 advantage. Democrats keep the Senate , however, and Democrat Rudy Perpich retains the governorship, which was not at stake this year.

Texas Republican lawmaking ranks have been increased by 17 - 1 in the Senate and 16 in the House. Both chambers, however, remain firmly in Democratic control. Gov. Mark White, who has two years left in his current term, also is a Democrat.

Republicans increased their ranks in 56 legislative chambers in 36 states. Democrats scored gains in 14 chambers in 12 states.

In only three of the latter - the Vermont and Montana Senates and the Alaska House - has this resulted in a shift of party control in the Democratic direction.

Montana, where the Republicans had held a 26-to-24 Senate edge, a four-seat switch give Democrats 27 to 23 control of the upper lawmaking chamber. At the same time, however, a five-seat Republican gain in the House brings the GOP even with its political opposition.

Vermont's newly elected Democratic governor, Madeleine Kunin, will have a 17 to 13 majority for her party in the Senate, a gain of four seats from the Republicans. The GOP, however, is retaining control of the House, 78 to 72; that's a six-seat slimmer margin than the party has had over the past two years.

In Alaska, where both lawmaking chambers had been GOP-controlled, the loss of three Republican seats - one to a Libertarian and two to Democrats - has given the Democrats a 21 to 18 majority in the House. Republicans retain an 11 to 9 edge in the Senate. Democratic Gov. Bill Sheffield has two years left in his term.

Democrats also boosted their legislative ranks by from one to three seats in Arizona, Hawaii, Indiana, Iowa, North Dakota, Rhode Island, South Dakota, Tennessee, and Washington.

A 10-seat Democratic gain in the already-Democratic-controlled Rhode Island Senate was offset somewhat by a seven-seat Republican increase in that state's lower legislative chamber, which stays in Democratic hands. Thus, newly-elected Republican Gov. Edward DiPrete will face lawmaking chambers dominated by the opposition.

Besides New Hampshire and Connecticut, those states with Republican majorities in both legislative chambers in 1985 are Arizona, Colorado, Indiana, Kansas, North Dakota, South Dakota, Utah, and Wyoming. Except for Indiana, South Dakota, and Utah, however, the governor is from the opposition party.

In contrast only 10 of the 27 states where Democrats outnumber the GOP in both lawmaking chambers have Republican governors. They are California, Illinois , Iowa, Missouri, New Jersey, North Carolina, Oregon, Rhode Island, Tennessee, and West Virginia.

The nine where one lawmaking chamber will be Republican and the other Democratic are Alaska, Delaware, Michigan, Minnesota, Nevada, New York, Ohio, Pennsylvania, and Vermont.

Also split, but in a different way, is the New Mexico legislature, where the two parties are tied in the Senate but Democrats control the House. Similarly, the Montana legislature is divided, with Democrats having a majority in the Senate and the House comprising 50 Democrats and 50 Republicans.