United States and Sweden warm up relations, both on and off court.

The Warsaw Pact began six days of military exercises in the Baltic Sea on Thursday, two days after similar naval maneuvers by Western powers. For neutral Swedes, whose western Baltic coastline has repeatedly been penetrated by Soviet spy submarines, the exercises serve as a reminder that the Nordic region is not exempt from East-West tensions.

This may offer a clue to the improvement in Sweden's relations with the United States, which was underscored during the visit earlier this week of Vice-President George Bush.

Despite differences on several issues, a new emphasis is being placed by both sides on the principle that Swedish neutrality should not interfere with friendlier ties.

A tennis match between Mr. Bush and retired Swedish tennis star Bjorn Borg can serve as a symbol of this shift. Just over 10 years ago, at the height of the Vietnam war, US-Swedish exchanges were sharp and accusatory in tone and took place on the diplomatic front rather than the tennis court.

Relations were nearly severed in 1972 when Prime Minister Olof Palme suggested the US was guilty of genocide when it resumed its bombing raids against Hanoi. Eventually, after the war, full contacts were restored and reconciliation began.

The extent of this process was evident in what Mr. Palme and Mr. Bush termed their ''open-hearted and frank'' discussions. The emotional tone of relations is increasingly approaching warmth. There remain serious differences between socialist-led Sweden and the conservative American leadership.

Mr. Palme's government is highly critical of US policy in Central America. And he has been a strident disarmament campaigner at the same time as the NATO allies have closed ranks behind the decision to install new missiles in Europe.

The Swedes have consistently rejected the concept of nuclear deterrence. Earlier this year, they proposed the creation of a ''corridor'' free of nuclear weapons between East and West as a confidence-building measure.

Stockholm has urged Denmark and Norway to relinquish their option, as members of NATO, to deploy nuclear weapons in wartime, and to accept proposals for a Nordic nuclear-free zone instead.

Both sides were careful not to let these differences poison the atmosphere. What resulted, a source said, was ''more a review and exchange than a debate.''

Swedish officials cite the end of the Vietnam war as the major factor behind the new relationship. ''It was without a doubt the most highly charged issue dividing us,'' a Foreign Ministry spokesman said. But other observers have also pointed to significant changes on the Swedish scene over the last decade.

The economic growth that provided one of the highest standards of living in the world and ''cradle to grave'' social protection has given way to uncertainty.

Serious questions have been raised in Sweden about the credibility of its defenses in the wake of repeated submarine incursions, and the inability of its Navy to force a vessel to the surface. There is a heightened recognition that security is closely linked to the stability of East-West relations.

This does not mean that the policy of neutrality, which has overwhelming public support, is being reconsidered. The last time Sweden ventured away from this stance was its unsuccessful attempt after World War II to form a Nordic defense association.