The United States and the Soviet Union will conclude six weeks of negotiations on nuclear and space arms in Geneva Tuesday with little progress to show, but evidently determined to press ahead in seeking a break in the deadlock when talks resume in late May.

The two sides appear to have clung tenaciously to past positions both in public and in private during the opening round of interrelated negotiations encompassing offensive strategic weapons, intermediate-range missiles and outer space missile defense systems.

Moscow's opening gambits have consisted of moratorium offers to halt deployment of nuclear arms as well as research and testing of space-based systems. Soviet negotiators have not shown any willingness to bargain or make concessions, apparently waiting for the United States to take the initiative.

The United States has spurned the freeze proposals, arguing that they would only preserve Soviet superiority. Meantime, U.S. negotiators have spent much of the first six weeks outlining the Reagan administration's "philosophy" of seeking deep cuts in offensive missiles now while emphasizing the future role of nonnuclear defensive measures that might include space-based systems.

But the Soviets have refused so far even to discuss the merits of the "strategic concept" as presented by Max Kampelman, head of the U.S. delegation.

The United States also has presented its objections to alleged Soviet violations of the Anti-Ballistic Missile treaty, particularly the phased-array radar system at Krasnoyarsk in central Siberia. The Americans charge that it could serve as an early warning or battle management system. The Soviets deny the radar is destined for military purposes and claim it will be used as a space-tracking station.

After returning to their capitals for a recess, U.S. and Soviet negotiators will begin a second round of talks on May 30. But substantive progress is not anticipated soon, even if a summit meeting is held this year.

While the mood at the negotiations became "more businesslike" toward the end of the round, the Soviet negotiators, who were said to have acted "a bit rougher" at the start than they did in previous negotiations, have not shown signs of exploring tradeoffs that might pave the way for a compromise.

There has been no discussion among the negotiators, even at informal lunches or receptions, of striking a "grand bargain" that could bring radical reductions in nuclear weapons in exchange for restraints on space arms.

The unyielding positions and tactics adopted by the Soviet delegation so far bear the signature of Foreign Minister Andrei Gromyko, whose negotiating methods are based on sticking to one view until the other side feels compelled to give ground first to reach an ultimate agreement.

As long as Gromyko masterminds Soviet arms control strategy, progress toward an agreement in Geneva is expected to be slow.

The ascendancy of Mikhail Gorbachev, however, has stirred speculation that he may be prepared to move more rapidly toward cutting an arms deal with the United States to free more resources to bolster the Soviet economy.

So far, Gorbachev has not made his mark in foreign or security affairs, repeating positions, even phrases, considered to be crafted in classic Gromyko style. But some senior western officials predict Gorbachev will extend his authority quickly in those areas because Gromyko no longer possesses the overwhelming power he wielded during the incapacitation of ailing Soviet rulers in recent years.

Nonetheless, Gorbachev's influence is not expected to become evident in the Geneva negotiations until the next Soviet Communist Party congress is held, probably early next year. By then it is believed he will have moved his personal allies into key positions and supervised the creation of the Soviet Union's next five-year military and economic programs, to be approved at the congress.

Thus a possible summit meeting this fall between Gorbachev and President Reagan is not expected, by itself, to break the impasse in the Geneva negotiations. But after the party congress, it is believed that Gorbachev may introduce more flexibility into the Soviet negotiating posture.

Sen. Ted Stevens (R-Alaska), cochairman of the Senate Arms Control Observers Group monitoring the Geneva talks, said he thinks there could be significant progress next year, leading up to an agreement "perhaps in the first five months of 1987."

In December 1983, the Soviets walked out of Geneva talks on intercontinental and medium-range nuclear weapons when NATO began deployment of Pershing II and cruise missiles in Western Europe to counter the Soviet triple-warhead SS20 missiles.

In agreeing to return to negotiations on March 12, Moscow insisted that the talks on strategic, intermediate and space arms are entirely new negotiations. During the opening round, Soviet negotiators did not budge in their demands that there be a "package deal," linking the fate of all three arms categories.

The United States has taken the position that progress in one area should not be held hostage to disagreements in others. But the Soviets have continued to insist in Geneva that an arms agreement is all or nothing.

The first six weeks of talks have produced no surprises, with both sides laying out their basic objectives or reiterating past proposals that were rejected previously.

In the space and defensive arms talks, led by Kampelman and Yuli Kvitsinky for the Soviet Union, the five meetings have been occupied largely with Soviet denunciations of SDI and the threat it poses to cause another spiral in the arms race.

In the strategic arms talks, conducted by Soviet delegation chief Viktor P. Karpov and former U.S. senator John Tower, the Soviets have called for a freeze on deployment of all strategic arms during the negotiations. But they have not responded seriously to U.S. calls to begin exploring possible formulas for tradeoffs in land-based missiles, where the Soviets are said to hold the edge, with long-range bombers and sea-launched missiles where the United States is superior.

In the medium-range weapons category, career diplomat Maynard Glitman has stressed the U.S. view that there should be a rough equality of missiles on both sides, with the Soviets allowed to deploy additional missiles in Asia to compensate for British and French nuclear missiles in the West.

His Soviet counterpart, Alexei Obukhov, has advanced positions already made public. These include Gorbachev's announcement of a halt in SS20 deployment until November, after which Moscow will decide what to do on the basis of the Pershing II and cruise missile buildup in Western Europe.