Orel Hershiser, Roger Clemens and Dwight Gooden are beginning their quests for the big bucks.

The three pitchers were among 132 players who filed for salary arbitration on Monday. In all, 136 players filed for arbitration this year, the second-highest total ever. After 1986, when 159 filed, rules were changed so that players needed three years, instead of two, of major-league experience to file.Hershiser, Clemens and Gooden could top the record arbitration-awarded salary of $1.975 million won by first baseman Don Mattingly of the New York Yankees last year.

Hershiser, the National League Cy Young Award winner and the Most Valuable Player of the playoffs and World Series for Los Angeles, was 23-8 with a 2.26 earned-run average and ended the season with a record 59 consecutive scoreless innings. He made $1.1 million last year.

Clemens, winner of the American League Cy Young Award in 1986 and 1987, was 18-12 with a 2.93 ERA and league-leading 291 strikeouts in 264 innings. He made $1.5 million in 1988 and recently rejected offers of $6.6 million for three years and $2.2 million for one year.

Gooden, who lost in arbitration last season at $1.4 million, was 18-9 with a 3.19 ERA. The Mets have offered a two-year contract with an option but Gooden wants three years at around $6 million.

Jose Canseco, the AL's MVP in 1988, was the top non-pitcher to file. He made $355,000 with Oakland last season and probably will seek a raise of more than $1 million. Players and clubs exchange figures on Thursday.

The New York Mets and California Angels each had nine players file, while Seattle, Montreal and Pittsburgh had eight each. At the othe end was Baltimore, which had only pitcher Mark Thurmond file. He won in arbitration last year.

Tom Henke of Toronto, John Franco of Cincinnati and Tim Burke of Montreal, relievers who lost their cases last year in their first test of arbitration, filed again.

Most players who filed will settle before hearings are heard from Feb. 1 to Feb. 20. Of 108 players who filed last year, 90 settled. Of the 18 that went to hearings, owners won 11 and players seven, the seventh consecutive year owners held the majority.

Outfielder Tony Armas of the Angels and pitcher Scott Bailes of Cleveland filed on Monday and agreed to one-year contracts later in the day. Armas will get the same $425,000 he made last year. Bailes will get $300,000, double his salary of last season.

Steve Lyons, the Chicago White Sox infielder, filed for arbitration even though he already has agreed to a one-year contract for $325,000. The contract calls for a reopener if he is traded later in the week. Pitcher Stu Cliburn of the California Angels also filed, although there is a grievance pending over whether he has sufficient major league service.