For a year, Gary Green has been trying to motivate the Washington Capitals' players to win games for themselves. Tuesday night he will ask them to win one for Gary Green.

Green and Coach Michel Bergeron of the Quebec Nordiques, who play the Capitals here Tuesday night at 7:30 (WTOP-1500), are bitter enemies, dating back to their days as rival coaches in the Memorial Cup, the Canadian junior championship.

"There is no team I'd like to beat more," Green said today when he was questioned about the feud. "When he was named coach, I promised I'd be motivated more for that game than any other. Nothing would make me happier than beating the little shrimp."

These are strong words from Green, normally a restrained individual who gets along with just about everyone. But he and Bergeron have had some shouting matches, both in person and in the newspapers, and there is the added fillip that Bergeron is a separatist, and Green is not.

The first encounter between the two took place during the 1978 Memorial Cup, played in the Northern Ontario cities of Sault Ste. Marie and Sudbury. Green coached Peterborough, the Ontario team that lost to New Westminster in the final. Bergeron, described in the Nordiques' press book as "le petit tigre," led Three Rivers, the Quebec entry that did not win any of its four games.

"I didn't know Michel Bergeron from a hole in the wall until that tournament," Green said. "We had some good games and he did a lot of yelling. There was screaming back and forth. He made some derogatory comments about our hockey club in the paper and he screamed at me during the games."

The following winter, Green coached Team Ontario and Bergeron guided Team Quebec in the Labatt Cup, a tournament played in several Ontario cities. Ontario beat Quebec in the final, 2-1.

"Our teams had some real battles and the final was an excellent hockey game," Green said. "But he complained viciously, cutting his own team up, calling them names in the papers. He blamed the rink, the building and even Ontario.

"What really burned me was that he would not stand behind the bench with his team for the Canadian national anthem. He's a separatist and he'd come out with the players and then leave.

"At the game in London, Bill Long and I had a bunch of security guards stand in the passageway to block him from leaving, but he banged through anyway.

"He was attacking me in the press and I blew off at him after the game. I told him he had a good hockey club and he should be proud of them, not ripped off at them. He was criticizing the whole tournament, even claiming he didn't get enough pucks in practice. I just said he was a big crybaby."

The two were at it again in the 1979 Memorial Cup, with Bergeron's Three Rivers team favored to win on its home grounds in Quebec. But after Three Rivers won its first two games, over Peterborough and Brandon, it fell apart and Green's Peterborough club wound up beating Brandon for the championship.

"He said he was going to get me that time and he called me a baby," Green said. "He said he wasn't going to lose to us again. They beat us the first game in their building, but we beat them in Sherbrooke and they didn't make the final."

Green went on to become the coach at Hershey, then was called to Washington to rescue the sagging franchise. Bergeron coached at Three Rivers one more season, then last summer was named an assistant coach with the Nordiques.

"I bit my lip at the NHI meetings when he was announced as Quebec's assistant and I stopped and offered congratulations," Green said. "We shook hands and I started to walk away. He said to somebody with him, "That is the man who called me a crybaby." I just turned around and shook my head." i

Six games into the current season, Bergeron relieved General Manager Maurice Filion as coach of the Nordiques, and here they are again.

"There isn't another coach in the league I dislike," Green said. But he certainly dislikes this one, which promises a frenetic time in Le Colisee.

Dennis Maruk has been named player of the week by the National Hockey League for his back-to-back hat tricks in Pittsburgh and Hartford . . . a quick check of league records indicated, however, that the feat was not so rare as had been first believed. It has been accomplished at least a dozen times, including three times this season -- by Darryl Sittler of Toronto, Mike Bossy of the New York Islanders and Maruk. . . Quebec will enter Tuesday night's game with a winless streak that has reached seven.