Republicans struck into their traditional mid-American heartland to make substantial gains in governorships and state legislatures in Tuesday's elections.

Although the Democrats still control a big majority of the gubernatorial seats and state legislatures, the GOP picked up a net of six governorships to boost its total to a reasonably respectable 18 statehouses. A decade ago, after Richard Nixon's presidential victory, the GOP had 31 governors but this had shriveled to 12 before Tuesday's gains.

In Ohio, veteran Republican James Rhodes retained office. In Pennsylvania, Republican Richard Thornburgh won, as did Republican Lamar Alexander in Tennessee. Democrats Jerry Brown (Calif.), Hugh Carey (N.Y.) and Ella Grasso (Conn.) were reelected, as was Republican James R. Thompson (Ill.). In a major upset, conservative Meldrim Thomson (R-N.H.) was beaten. In Texas, Republican William Clements won.

In the state legislatures, according to tabulations by the National Conference of State Legislatures, Republicans started out on Tuesday with two-chamber control of legislatures in six states and a split in eight others. The remining 36 were held by Democrats in both chambers.

Democrats didn't pick up a single state legislative chamber on Tuesday, and by the end of the day, Republicans controlled both chambers in 13 states. To to it, they took both houses from the Democrats in Iowa, one from them in Arizona, Indiana, Utah, North Dakota, Vermont and Kansas.

In six other states, they ended the day with one chamber in tow, or virtual ties for at least one chamber, (Illinois, Maine, New York, Minnesota, Pennsylvania and Washington). In 30 states Democrats held both chambers; Alaska results weren't complete.

Democrats had previously held 5,100 state House or Senate seats, Republicans 2,400. Republicans, who spent $2 million on candidates like Jim Butcher of Indiana in state elections to boost their position, picked up about 250 state legislative seats net nationwide. (Butcher, political newcomer typical of GOP recruits, won his race for the Indiana Senate.)

These gains in governorship and legislative races, while not overwhelming, put the GOP in a better position to use state power and patronage in an attempted nationwide comeback for Congress. GOP Chairman Bill Brock called it "an outstanding day" for his party.

In the governor races, many nationally known incumbents won as expected. In Ohio, Rhodes shattering hopes of the Democrats for the fourth time since 1962, narrowly beat Lt. Gov. Richard Celeste in a race with the lowest turnout since 1954.

Rhodes a skillful political infighter, was helped by what one reporter called political exhaustion in Cleveland, where Mayor Dennis Kucinich has been the subject of a recall petition and constant fights with other politicans.

The indictment by a Democratic prosecutor of six city councilmen - five of them black - on various financial charges hurt the Democrats among the traditionally Democratic black voters. Rhodes accused Celeste of wanting to double people's taxes after Celeste hinted at lowering property taxes but boosting income and business taxes.

Also winning were other nationally known names like incumbents Robert Ray (R-Iowa)) and William Milliken (R-Mich.).

In Tennessee, 38-year-old Nashville lawyer Alexander captured the governorship for the GOP, whipping wealthy Democratic banker Jake Butcher.Alexander, who has been a political commentator on a television station in middle Tennessee (Nashville and surrounding area), a traditional Democratic stronghold, did particularly well in that area aided by his TV recognition.

Tennessee political observers said Butcher was also hurt by previous financial scandals in the administration of outgoing Democratic Gov. Ray Blanton and by his own refusal to make full public disclosure of his finances.

Another closely watched race occurred in Massachusetts, where conservative Edward King, 53, a surprise primary winner over the incumbent Democratic governor, easily beat Republican Francis Hatch, a wealthy Republican. King won with a well-organized campaign, espousing a $500-million tax cut, opposition to abortion and busing and support for capital punishment - stands which observers said gained support among Irish and Italian low-income voters already suspicious of the wealthy "Yankee" Hatch.

Another factor in King's victory was the all-out support of House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), whose son Tom was running for lieutenant governor on the King ticket. For young O'Neill to win, King had to win too and Tip helped make it so.

The GOP picked up these governorships previously held by Democrats:

Minnesota, where Rep. Albert Quie beat incumbent Gov. Rudy Perpich.

Nebraska, where Rep. Charles Thone took the seat.

Nevada, where Robert List was the winner.

Oregon, where Victor Atiyeh ousted incumbent Robert Straub.

Pennsylvania, where former Justice Department prosecutor Thornburgh beat former Pittsburgh mayor Pete Flaherty in an upset.

South Dakota. where Attorney General William Janklow took the seat.

Wisconsin, where unorthodox professor Lee Dreyfus won.

Tennessee, where Alexander was the winner.

Texas, where Clements, a former deputy secretary of defense, won.

The Democrats, while dropping those seats to the GOP, beat Thomson in New Hampshire, saw John Carlin (D) beat incumbent Republican Robert Bennett in Kansas and recaptured the South Carolina governorship. The also recaptured Maine, which had been held by an independent.

As a result of the election. Democrats will hold 32 governorships, Republicans 18.

In local races of more-than-routine interest, former Rep. Wayne Hays (D Ohio), 67, who left Congress two years ago after a sex scandal, squeaked into the Ohio House by a narrow margin in a political comeback try.

Also in Ohio, Anthony Celebrezze, son of the former Democratic U.S. Secretary of Health, Education and Welfare, finished slightly ahead of his GOP opponent for secretary of state, but a recount is expected.

In New Mexico, Jay Alan Hartke, son of former senator Vance Hartke (D-Ind.). was elected state treasurer.

In New York, Democrat Harrison Goldin, running for comptroller on Carey's ticket, was beaten by Erie County executive Edward Regan.

Barbara Bailey Kennelly, daughter of the late Democratic National Chairman John M. Bailey, was elected Connecticut Secretary of State.

Richard C. Erwin won a statewide race for the North Carolina Court of Appeals, the first statewide victory for a black since Reconstruction. Another black, former Pittsburgh Steeler defensive end John H. Baker Jr., was elected Wake County, N.C., sheriff.

Hawaii got its first woman lieuetnant governor, Democrat Jean Sadako King, and Colorado got its first woman attorney general, Nancy Dick of Aspen.