One of the largest, most bitter labor disputes in U.S. history may be nearing an end.

The Amalgamated Clothing and Textile Workers Union has reached a tentative contract agreement with J.P. Stevens & Co. Inc. -- for nearly two decades the symbol of anti-unionism in the South.

The new agreement, scheduled to be announced Monday at AFL-CIO headquarters, would provide contracts for the handful of Stevens plants where the union has won certification and agreement on procedures for the union to try to organize all other Stevens plants, sources said yesterday.

Officially, both the company and the union denied that any agreement had been reached."There is no agreement right now," union spokesman Burt Beck said. Stevens spokesman James Franklin also insisted that no agreement had been reached. Both sides conceded that active negotiations were under way, however.

"They've reached agreement on everything but a few minor issues," a source close the negotiations said. "They've only got a few 'i's to dot and some 't's to cross."

Precise details of the agreement were not available yesterday. But sources said the new contracts would cover the Stephens plants in North Carolina where the union had won recognition.

More important for the union, the final agreement is expected to contain ground rules under which the company would allow the union to try to organize all its other plants. J. P. Stevens is the nation's second-largest textile manufacturer.

Both sides are expected to name a nationally recognized arbitrator to police the organizing agreement. The name of the arbitrator was not known.

Union members at Stevens plants in such places as Roanoke Rapids and High Point, N.C., are expected to vote on the new contract Sunday.

Ratification would mark the end of a bitter union struggle against J. P. Stevens that was begun 17 years ago by the Textile Workers Union of America. In the nearly two decades since, the campaign to unionize J. P. Stevens has become a major cause of the American labor movement.

Reports of violence and worker mistreatment -- which gained national attention recently in the movie "Norma Rae" -- were the hallmark of almost every major union meeting in recent years.

Despite labor's lip service to the Stevens campaign, the organizing drive did not begin in earnest until 1976, when the textile union merged with the larger Amalgamated Clothing Workers Union. That union, fresh from a major organizing victory in the Southwest against the Farah Co., committed almost all its organizing resources to the Stevens campaign.

Using the same tactic that brought them victory at Farah, Amalgamated organizers launched a consumer boycott against Stevens' products in 1977, along with a successful campaign to embarrass leaders of other major corporations who were on Stevens' board of directors and to steer union pension funds away from any organization doing business with Stevens.

The latter tactic appears to have put the most pressure on Stevens. Alghough the consumer boycott received a lot of publicity, few of Stevens' products are consumer goods.

The success of the union's boardroom tactics was best seen last summer, when Stevens accused Amalgamated organizers of being "terrorists" after an unsuccessful attempt to have Stevens Chairman James D. Finley removed from the board of the Sperry Corp.

Any agreement between Stevens and the union will not make the organization of other Stevens plants automatic. Company officials are expected to do everything they can do to keep the union out of the other plants. But the new agreement is expected to end the years of tactics the company has been using to keep the unions out. Stevens has been cited repeately for violating the National Labor Relations Act.

Textile union officials long have seen a victory at Stevens as the key to opening the gateway to the South, which traditionally has shunned trade unions. When the agreement is announced, it will be hailed as just that.