Who gets credit for keeping the Soviet bear at home?

At his press conference this week, President Reagan seemed to take credit for halting for nearly two years Soviet advances around the world.

The President thus put himself at odds with a number of American experts on the Soviet Union, both outside the Reagan administration and within it. Those experts say the lack of Soviet advances in the third world and elsewhere can be attributed more to three factors - a lack of opportunity, the drain of Poland and Afghanistan, and the Soviet leadership transition - than to anything else.

But when asked at the Sept. 28 press conference how he would assess the state of relations with the Soviets 20 months after he took office, Mr. Reagan said, ''I think there's a pretty good understanding on their part as to where we stand , and I can say only this: In 20 months - and I'm going to knock on wood - the Soviet Union, which has been expanding over the years vastly in the territory and the people coming under its control, they haven't expanded into an extra square inch since we've been here. So maybe we do have an understanding of each other.''

One expert who says he thinks ''an element of outright fear of the Reagan administration'' has contributed to Soviet restraint around the world is William G. Hyland, a former deputy national security adviser in the Nixon and Ford administrations. He is now a senior associate at the Carnegie Endowment for International Peace.

But Mr. Hyland, one of those whom Secretary of State George P. Shultz has consulted on Soviet affairs, also says a lack of third-world opportunities and the all-consuming internal struggle for succession to Soviet President Leonid I. Brezhnev are other factors that have contributed to Soviet restraint.

''I think it smacks of election-year demagoguery for Reagan to claim that this administration has stopped the Soviets because of the position he's taken, '' said Richard T. Davies, a career diplomat and former ambassador to Poland who served twice at the US Embassy in Moscow. ''To my way of thinking, this administration actually contributed to the crackdown in Poland.''

''The administration's principal act was to lift the partial grain embargo against the Soviet Union,'' said Davies. ''I'm afraid that gave the Soviet leadership, and the Polish leadership, the signal that they needed. They then knew that there would be no sharp response from this administration if the Polish internal forces - not the Soviets - cracked down.''

''Fortunately for us, there is a period of relative foreign-policy passivity . . . but none of it is to the credit of the Reagan administration.''

During his press conference, Reagan also took note of talks between the US and the Soviets. He mentioned that Secretary Shultz met for three hours in New York on Sept. 28 with Soviet Foreign Minister Andrei Gromyko. Reagan noted that in a telephone call, Shultz had told him that the discussion with Mr. Gromyko was ''serious'' and ''wide-ranging.'' The two officials are to meet again on Oct. 4, Reagan said.

''. . . So we're not standing off and ignoring each other,'' the President said.

''What the President did not say is that since he took office, emigration - mostly Jewish emigration - from the Soviet Union has dropped to a virtual trickle from a high point of thousands each month,'' said Jonathan Sanders, assistant director of the Russian Institute at Columbia University.

''He also failed to mention that the opportunity for American businessmen to earn money in the Soviet Union is now virtually nil,'' Mr. Sanders says. ''He failed to mention that cultural exchanges with the Soviet Union have come to a halt. And he did not mention that his administration's ideological hostility toward the Soviet Union, as evident in its pipeline policy, has done something to the NATO alliance that the Soviet Union has not been able to do for all these years - tear the alliance at the seams.''

Mr. Hyland, for one, thinks that the failure of the Western allies to reach agreement over West Europe's gas pipeline trade with the USSR has given the Soviets opportunities to exploit in Europe and has diverted the alliance from dealing with more important matters, such as East Europe's debts.

Nearly everyone in Washington seems to agree, in the meantime, that one third-world test for US-Soviet relations will be the Soviet attitude toward the southern African nation of Angola and the Cuban troops stationed there. State Department officials are still uncertain whether the Soviets will play a ''spoiler'' role or stand aside and allow the Cubans to depart as part of a Namibia settlement.