Ronald Reagan holds his popularity despite the hostage incident, at least for now. There's also increasing likelihood of a US-Soviet summit, as Gorbachev takes charge in the Kremlin. Can hostage homecoming help Reagan politically?

Ronald Reagan averted the problems of Jimmy Carter. But whether the President's success in bringing home 39 American hostages will translate into a political benefit to his second-term agenda is an open question.

GOP strategists foresee at least a short-term gain for Mr. Reagan. ``It's a definite plus for the President,'' says James Lake, who served with the '84 Reagan-Bush election campaign. ``He comes out better than when he went in, and in the long run, anything that adds to his popularity enables him to govern.''

But many political observers view the hostage crisis as a momentary blip on the screen, after which Reagan will again confront the hard political realities of dealing with tax reform and the budget deficit. The American public has not enthusiastically embraced the tax-overhaul plan, and concern about the federal deficit is growing -- with more and more talk heard these days about a tax increase.

``Reagan comes out of this having minimized the damage, and that enables him to get back on track with his presidency,'' says political scientist Thomas Mann. ``The President remains a powerful political commodity, and this recent experience maintains that stature. But the problems he is having with tax reform and budget matters have nothing to do with his popularity. The battles now are being waged on the merits -- on how various interests are affected.''

``You can't view this as a great triumph for Reagan,'' says Norman Ornstein, a political expert at the American Enterprise Institute. ``Things did not go beyond the point where the rally-round-the-President mood turned to bitterness. But after the initial euphoria is gone, . . . it will be seen that once again we were kicked in the rear and humiliated.''

``The negatives from that will balance out the positives,'' Mr. Ornstein says.

Polls show that most Americans approve of the way Reagan handled the hostage crisis. A Harris survey released Tuesday shows a 53 percent positive rating for the President during the ordeal and a 57 percent approval after release of the hostages. The President is also given more credit than Shiite leader Nabih Berri or Syrian President Assad for the release.

At the same time the public appears bewildered by the phenomenon of terrorism. Many Americans, though not most, believe the Beirut incident was more a victory for the Shiite hijackers than for the US, according to a Washington Post/ABC News poll this week.

The White House is conscious of the ambivalent American mood. In light of the fact that one hostage did not return and seven other Americans have yet to win their freedom in Lebanon, White House officials seemed determined to avoid a splashy homecoming celebration. The President was scheduled to welcome home the Americans Tuesday in a low-key ceremony at Andrews Air Force Base in Maryland, meeting privately with the Americans aboard their plane and then delivering brief public remarks.

Almost as if to minimize news-media attention to the former hostages, the administration also indicated Tuesday that Reagan will hold a summit conference with Soviet leader Mikhail Gorbachev in the fall. Administration officials said the meeting will take place in Geneva from Nov. 19 to 21, according to the Associated Press.

There is a difference of opinion about how much damage the President sustained by being sidetracked from his tax-reform crusade. Ornstein suggests the President wanted to focus on the congressional budget conference before the July 4 recess. Now any leverage he had has dissipated. Meanwhile, momentum on tax reform has flagged.

``The delay will simply give the President a little less leverage and put more in the hands of those want other things,'' Ornstein says.

Other analysts do not see an appreciable setback for Reagan because of the hostage crisis. Stephen Wayne, a presidential scholar at George Washington University, says he thinks the House-Senate budget compromise will be ironed out without the President and that Reagan, by becoming involved, would simply show how little power he has in this particular battle.

As for tax reform, says Dr. Wayne, the President has time to come back to that. Moreover, instead of losing any influence on Capitol Hill because of the Beirut crisis, he may find Congress more amenable now to covert actions.

``But he does not come away from the hostage crisis looking good,'' says the political scientist. ``And if terrorism persists and his actions cannot prevent it, I see his approval declining.''

Opinion experts note that the principal concern about Reagan during the 1980 campaign was that he would prove to be a belligerent, trigger-happy leader in foreign affairs. Yet, while a majority of Americans do not favor military retaliation, there is a measure of frustration with the administration for being too soft. According to the Washington Post/ABC News poll, 36 percent of Americans think the President was not tough enough in the Beirut crisis.

``That's an interesting switch when compared to the first year of the presidency,'' says opinion analyst Everett Carll Ladd of the University of Connecticut. ``That means that this administration is not politically vulnerable to that kind of criticism.''