Whenever President Reagan finds himself in political difficulty, his instinctive and time-honored remedy has been to solve his problem with a speech.

Today, trying to dampen one of the most troubling controversies of his presidency, Reagan gave two speeches. While neither measured up to the extravagant advance billing of White House advisers, the president's performance served his purposes of demonstrating that he understood both the "uniquely destructive" nature of the Holocaust and the critical importance of postwar reconciliation.

At Bergen-Belsen, where his voice was muted and sometimes strained, Reagan talked of the killing of children and the murder of Jews, "whose death was inflicted for no reason other than their very existence."

At Bitburg Air Base, where Reagan's spirits rose in the presence of bands and approving U.S. military families, he came as close as he ever has in a major speech to admitting that he might have made a mistake.

The president acknowledged that his decision to lay a wreath at a German military cemetery had "opened old wounds" during a visit that was supposed to be "a time of healing." He assured Jews that reconciliation did not mean forgetting Nazi crimes. Earlier in the week Reagan had confided to an intimate that he was frustrated and angry over being depicted as insensitive to the Holocaust after 40 years of speaking up about "Nazi crimes" against the Jews.

Afterward, Reagan called the day one of "hope and remembrance," but his uncharacteristically sober mien seemed to say that it was also a difficult ordeal. The words of Reagan's speech at Bergen-Belsen proclaimed that "horror cannot outlast hope," but Reagan appeared somber rather than hopeful much of the day.

Before he spoke he had walked through the camp's Document House and viewed the photographs of stacks of corpes, then strolled through a series of memorials above mass graves.

Reagan always has been sensitive to the notion that he is a former actor who can weep on cue. At Bergen-Belsen he appeared to be trying not to cry, almost trying not to act, as he gave a speech recalling "the monstrous, incomparable horror" of the camp.

But his voice broke nonetheless as he read from a famous passage in the diary of Anne Frank, a 15-year-old Dutch Jew who died at the camp, which said, "I still believe that people are good at heart."

Reagan prefers to speak from notes or a teleprompter. Today, he appeared hampered in his delivery, particularly at the ex-concentration camp site, by having to read from a prepared text.

He had one minor slip, referring to the camp as "Berger-Belsen" and added one brief passage in which he said he had reflected, as he flew in from Hanover over the green countryside, that "there must have been a time when the prisoners at Bergen-Belsen, and those at every other camp, must have felt the springtime was gone forever from their lives."

In his subsequent Bitburg speech, written a week ago, Reagan read from another text describing his visit to Bergen-Belsen and saying he had felt "great sadness" there.

Reagan's speeches, largely crafted by his premier political speech writer Kenneth Khachigian, were notable for what they omitted as well as what they said.

At Bergen-Belsen, where more than 60,000 civilians, including 30,000 Jews, perished, Reagan made no mention of the 50,000 Russian prisoners of war who died there earlier in the war.

And at Bitburg, Reagan converted his call for reconciliation into a familiar attack on communism when he recalled president John F. Kennedy's declaration that he was a Berliner and went on to compare himself to a Jew, an Afghan, "a prisoner of the Gulag," a Vietnamese refugee, a Laotian, a Cambodian, a Cuban and a Miskito Indian in Nicaragua.

Reagan did not mention the Soviets by name. He also did not mention Adolf Hitler, although he portrayed the crimes of Nazism as the evil work of "one man," an act of deference to his German hosts.

While some of the president's aides publicly and effusively praised the speeches -- Assistant Secretary of State Richard R. Burt called them "a brilliant performance" -- the private expectations of the president's advisers were more subdued.

When the White House launched its damage-control campaign last week to extricate Reagan from the Bitburg controversy, a senior official said, "We can't make a plus of it, but we can ameliorate the damage."

The expectation of Reagan's strategists was that a satisfactory performance by the president in his two speeches and a quick cemetery ceremony would subdue the controversy and allow Reagan to proceed to other things.

The White House has been buoyed by surveys taken by veteran Reagan pollster Richard Wirthlin said to show the president's popularity holding firm in the face of Bitburg. Some other surveys, however, give conflicting results.

While it probably will be days or weeks before it becomes clear whether Reagan has succeeded in putting Bitburg behind him, the controversy has left two legacies.

One is a conspicuous deterioration of relations between the president and the press, whom Reagan and his chief aides blame for blowing the incident out of proportion.

The other is an unaccustomed defensiveness in the Reagan White House, which has suffered a string of defeats on budget matters and foreign policy. Reagan's more sensitive strategists recognize that Bitburg could become the symbol of a declining presidency if Reagan cannot reverse his fortunes.