WASHINGTON (AP) _ Republicans are almost certain to score gains in governor's races Tuesday, but it would take a sweep of 10 tossup contests for them to come out of the 1986 elections with their goal: a majority of the nation's governorships.

A survey of the races by Associated Press reporters in the 36 states electing governors this year found Democratic candidates appeared safe in 11 states and leaning ahead in two more.

In five states the Republican was safe and four more states were leaning GOP.

The remaining 14 states, a surprisingly large number, remain tossups going into Election Day. But Republicans must win 10 of those 14 neck-and-neck races if they are to capture a gubernatorial majority for the first time since 1969.

''There's just too many close ones to call,'' said Chuck Dolan, director of the Democratic Governors' Association.

In an election-year arithmetic that favors the GOP, Democrats find themselves defending 27 of the 34 governorships they now hold. The GOP, with but 16 governors, defends only nine.

The races that could go either way on Tuesday are largely in states now held by Democrats - Florida, South Carolina, Texas, Nebraska, Kansas, Hawaii, Arizona, Alaska, Wyoming, Alabama and Wisconsin.

Three of the too-close-to-call races are in states now held by the GOP: Oregon, Tennessee and Pennsylvania.

Most of the endangered Democratic governorships are being vacated by popular incumbents. But two Democratic incumbents are trying to withstand fierce GOP opposition - in Texas, where Gov. Mark White still slightly trails the man he defeated four years ago, former Gov. Bill Clements; and Wisconsin, where Gov. Anthony Earl has been pressed by Republican legislative leader Tommy Thompson.

The Democrats' most prominent governor, possible presidential candidate Mario Cuomo of New York, has an easy race for his second term. Also expected to win are Democratic incumbents in Michigan, Minnesota, Nevada, Massachusetts, Georgia, Arkansas, Connecticut and Ohio. Also regarded as safe are Democratic candidates in Idaho and Maryland.

In Vermont, Democratic Gov. Madeleine Kunin is leading but could fall short of the 50 percent she needs to keep the three-way race from being decided by the legislature. Colorado, a state the GOP had hoped to gain, also leans Democratic.

California Gov. George Deukmejian appears likely to win a second term against Los Angeles Mayor Tom Bradley, one of two candidates seeking to become the first black elected governor. The other black is long-shot GOP nominee William Lucas in Michigan.

Republicans also appeared safe in New Hampshire, Rhode Island, South Dakota and New Mexico.

Among states leaning Republican, Illinois Gov. James Thompson was leading over Adlai Stevenson, a Democrat running under a third-party banner. Republicans also were leading in Iowa, where Gov. Terry Branstad has distanced himself from Reagan farm policies in the face of a strong Democratic challenge, and in Maine and Oklahoma.

Acknowledging probable losses, Democratic National Committee chairman Paul Kirk is predicting Democrats will end up with 30 governorships, a loss of four. Dolan said losses could be four to eight.

Retiring Pennsylvania Gov. Richard Thornburgh, chairman of the GOP governors' campaign committee, said a majority is the goal but attainable only as a best-case scenario.

''What we're looking at is a reasonable figure of six, and with a few breaks, eight to 10,'' he said.

Here is a look at the states that appear the closest:

ALABAMA - A confusing, bitter internal Democratic brawl has given Republican Guy Hunt, a 3-to-1 loser eight years ago, a chance to become the first GOP governor since Reconstruction. Attorney General Charles Graddick won the Democratic nomination but was bumped off the ticket in a court fight in favor of Lt. Gov. Bill Baxley. Graddick called off a write-in campaign last week, but voter animosity toward the Democrats is high and Hunt has led in one recent poll.

ALASKA - Republican state Sen. Arliss Sturgulewski, one of nine women on gubernatorial ballots, is facing Democrat Steve Cowper, who defeated incumbent Gov. Bill Sheffield in the primary. Sturgulewski's chances have been hurt by a last-minute write-in campaign by primary loser Walter Hickel, a former governor who is likely to take GOP votes.

ARIZONA - This is a three-way race between Democrat Carolyn Warner, the state school superintendent; far-right Republican Evan Mecham, an upset primary winner over the GOP establishment candidate; and Bill Schulz, an unpredictible onetime Democratic candidate who pulled out, then got on the ballot as an independent after Warner's nomination. New polls show the candidates running neck, neck and neck.

FLORIDA - Former Tampa Mayor Bob Martinez, recent convert to the GOP, is facing Ivy-League educated Democrat Steve Pajcic in a hard-fought race. Pajcic is supported by environmentalists and is accused of being too liberal by Martinez, who could become the state's first Hispanic governor. It's an extremely tight race, with latest polls showing a slight edge for the Republican.

HAWAII - Democrat Lt. Gov. John Waihee faces Republican former legislator D.G. ''Andy'' Anderson. Waihee is identified with three-term Gov. George Ariyoshi in this Democratic-voting state, while Anderson has argued he is the candidate of change.

KANSAS - Democrat Lt. Gov. Thomas R. Docking and Mike Hayden, the GOP House speaker, are in a tight race in which Docking claims he has a better vision of the future while Hayden cites his long experience in the legislature. Docking's father and grandfather were governors.

NEBRASKA - This close race features two women, Republican state Treasurer Kay Orr and Democrat Helen Boosalis, former mayor of Lincoln. Taxes has been a major issue, with Orr trying to link Boosalis with a sales tax increase proposal. This race could be as close as the 6,500-vote squeaker the Democrats won four years ago.

OREGON - Democrat Neil Goldschmidt, former transportation secretary in the Carter administration and Portland mayor, is facing former secretary of state Norma Paulus in this GOP-held state. The slumping economy is the issue in what is regarded as a dead heat.

PENNSYLVANIA - Republican Lt. Gov. William W. Scranton III's age, 39, and his acknowledgement that he once used ''recreational drugs'' were issues in his race to take the seat being vacated by Thornburgh. Although polls showed Scranton with a large lead early on, it evaporated as the campaign of Democrat Robert P. Casey, a former auditor general, picked up steam.

SOUTH CAROLINA - Rep. Carroll Campbell, a bright star of the South's GOP, is waging a hard battle to wrest control of the statehouse from the Democrats, who hope to elect Lt. Gov. Mike Daniel.

TENNESSEE - Former Republican Gov. Winfield Dunn and Democrat Ned Ray McWherter, speaker of the Tennessee House, are running neck-and-neck. The race has been highlighted by charges about their personal financial dealings.

TEXAS - White faces a stiff challenge from Clements, who lost the governorship to White in 1982. Texas's economy, dragging because of a the drop in world oil prices, is the major issue, and a double-digit Clements lead has shrunk. The race has been marked by a mysterious electronic bugging device found in the office of a Clements' campaign strategist.

WISCONSIN - Earl, seeking re-election to a second term, faces a tough challenge from Thompson, who claims the state has lost business and attracted people on welfare during Earl's administration.

WYOMING - With Democratic Gov. Ed Herschler retiring, Republican Peter K. Simpson, son of a former governor and brother of Sen. Alan Simpson, hoped to take the seat for the GOP. But a bruising primary which Simpson won by 453 votes splintered the GOP, boosting the chances of Democrat Michael Sullivan.