President Reagan began his second term last January calling for a balanced budget and "the total elimination one day of nuclear weapons from the face of the earth." A year later, after numerous bouts with Congress and his first summit meeting with a Soviet leader, he has taken only the first, tentative steps toward achieving those goals.

For Reagan, 1985 has been a mixed and often frustrating year. He currently enjoys some of the highest public approval ratings of his presidency, but he has not been able to translate that popularity -- or the strength of his landslide reelection triumph -- into notable victories on Capitol Hill. On the contrary, he was forced repeatedly to compromise with Congress this year, and some of the victories he achieved -- the tax revision vote is the most recent example -- came only after the administration was threatened with a humiliating defeat.

"You know what the saving grace has been?" said one of the president's senior political advisers. "The TWA hostage crisis, the summit and cancer."

Sen. Paul Laxalt (R-Nev.), a Reagan intimate, said, "Considering what past presidents have done in the first year of the second term, it was a vintage year . . . . The summit was, overall, deemed a smashing success. Couple that with his artificial resuscitation of tax reform when everyone -- including me -- thought it was truly dead. He went out in a blaze of glory. Next year could prove to be far more difficult."

Mitchell E. Daniels Jr., the White House political director, said that Presidents Dwight D. Eisenhower and Richard M. Nixon had more trouble in their fifth years than Reagan had. "Even if it wasn't always pretty this year," Daniels said, "when you run up the tally board, the stuff we wanted is happening, and the stuff we didn't want, isn't."

This was the year Reagan's top political strategists had seen as a second-term "window of opportunity" -- the best period to win approval of his domestic agenda, including tax revision, and to renew dialogue with the Soviet Union before he became weakened as a lame duck.

But that "window" involved months of inconclusive bickering over budget cuts between Reagan and Congress that finally resulted in the Gramm-Rudman-Hollings legislation, which is expected to force both sides to make the difficult choices they have so far avoided.

Reagan also used the "window" to engage Soviet leader Mikhail Gorbachev in the first U.S.-Soviet summit of his presidency. After years of harsh criticism of the Soviets, Reagan began a "dialogue" with Gorbachev that did not bring about an arms control pact, but did produce an agreement to hold two more summits and generated hopes that the two superpowers may yet achieve a far-reaching treaty to reduce their nuclear arsenals.

The first year of Reagan's second term brought other unexpected challenges for a president trying to cement his place in history and postpone the inevitable day his political power begins to wane.

His vaunted vitality was tested by a serious bout with cancer. His command over Congress was threatened at year's end by the near-collapse of his tax revision bill. He endured an emotional, if not lasting, controversy over his visit to a German military cemetery at Bitburg. And two Middle Eastern hostage crises -- the hijackings of TWA flight 847 and the Achille Lauro cruise ship -- tested the administration's ability to cope with and retaliate against terrorists.

After nearly two years of internal debate over the use of military force against terrorism, Reagan last fall decided to send American fighter jets after the hijackers of the cruise ship, and emerged triumphant from the successful interception.

But in dealing with Congress, Reagan enjoyed little of the honeymoon atmosphere that existed after his first election in 1980. Instead, the president battled defensively to preserve what he had won earlier.

He accepted a smaller MX missile force and no growth above the rate of inflation for the Pentagon budget, and invoked limited sanctions against South Africa when it was clear that Congress was prepared to legislate tougher action. He won resumption of aid to the Nicaraguan rebels, but military help was barred. He dampened the trade protectionism tide in Congress, partly by reversing policy and seeking to gradually lower the value of the dollar.

His major triumph -- House approval of a tax bill -- came only after a damaging Republican revolt.

"Everyone talks about the honeymoon, but the honeymoon and the fifth anniversary aren't the same thing," said Dennis Thomas, deputy to White House chief of staff Donald T. Regan and an increasingly influential adviser. The last five months, he said, "were one big land-mine field, and we've extricated ourselves from it."

"In each instance, they had Reagan down and out -- on South Africa, trade, appropriations bills and tax reform," he said. "Mark Twain must be amazed at the number of times Ronald Reagan's political demise has been prematurely reported."

But Reagan made little headway this year in permanently reducing domestic spending. After the election, he proposed the most ambitious budget-cutting program of his presidency, seeking to trim or eliminate many government programs that provided subsidies to business and the middle class.

"The basic record there is not much success," said political scientist Norman J. Ornstein of the American Enterprise Institute. He said Reagan and former budget director David A. Stockman wanted to use the "momentum" of the reelection landslide to attack such programs as Amtrak and the Small Business Administration, but "now at the end of the year, after going through the agonizing budget process, Amtrak and the SBA are still intact."

A White House official acknowledged that the effort failed. "The waves pounded on the shore, and the shore won," he said. "The answer is that the great bulk of the effort, 50 major reductions and terminations, were not achieved. The major fiscal and philosophical goal was to really take a serious large whack out of domestic spending, and we got very, very little."

One reason was that Reagan did not lobby as strenuously for politically painful budget cuts as he did in 1981, nor had he sought a mandate for such action during his reelection campaign.

Also, Reagan made deals -- first with the Senate and later the House -- to take certain proposed budget cuts off the table. Then, when Congress adjourned for the year, it left without finishing work on the one piece of legislation implementing the program cutbacks it had approved.

Reagan may have reached a turning point on defense spending this year. He began by seeking 6 percent growth in Pentagon spending authority over inflation -- and wound up accepting zero growth. Most of the actual deficit savings achieved this year came out of Reagan's military budget, and even with the savings, next year's deficit is projected to exceed $194 billion.

More important, however, Reagan accepted the Gramm-Rudman-Hollings measure designed to force a balanced budget by 1991. Many administration analysts say the legislation will mean, along with further reductions in domestic spending, cuts in Reagan's planned defense buildup or a tax increase.

"It may come down to a wire -- compromise further on defense or look for revenues," Laxalt said. "That's going to be difficult for him."

Reagan acquiesced on Gramm-Rudman-Hollings, in contrast to his first-term posture of pushing Congress on major legislation. Ironically, the action may be remembered as the point at which deficit reduction became Reagan's top priority, rather than tax cuts and more defense spending.

"We're alive to fight another day," White House aide Daniels said.

"Almost in spite of themselves with Gramm-Rudman, they are back in the ball game," Ornstein said.

On arms control, Reagan this year started a process that may hold the promise of future results. Standing in a parking lot in Geneva, he and Soviet leader Gorbachev agreed to the additional meetings that may create pressure for more solid accomplishments.

"The get-acquainted stage is over and people are going to start looking for concrete results," Laxalt said.

One lesson of 1985, even for some of Reagan's closest advisers, was his deep commitment to the idea of a space-based nuclear shield against incoming missiles, the Strategic Defense Initiative (SDI), often called "Star Wars."

Earlier this year, some White House advisers privately discussed possible limits on SDI in exchange for deep cuts in the Soviet offensive missile force. But Reagan forcefully ruled it out at a Sept. 17 news conference, and two months later at the summit sharply differed with Gorbachev on missile defenses.

Sen. Albert Gore Jr. (D-Tenn.), said the "one big positive" development this year on arms control was Reagan's decision to continue U.S. policy of not undercutting the SALT II accord.

But Gore criticized Reagan's intransigence on SDI, saying "the continuing internecine warfare" in the administration over arms control "has prevented the president from seizing a number of promising opportunities that should have been explored."

"The apparent decision to show no flexibility whatsoever on SDI has threatened to bring all arms control to a standstill," Gore said.

Raymond L. Garthoff, author of "Detente and Confrontation: American-Soviet Relations from Nixon to Reagan," said that while many doubt whether an invincible shield against missiles is possible, "That still is the way Reagan is talking. I think he has concluded that he stood firm at the first summit, things went pretty well. That's all true as far as it goes. What bothers me is he'll be all the less likely to think he should compromise."

In presummit exchanges and later at Geneva, the superpowers agreed on the concept of a 50 percent cut in some categories of offensive weapons, but remained far apart on critical definitions of what would be included. Reagan and Gorbachev also agreed to press ahead in areas where they believe some common ground exists -- such as the talks on medium-range missiles in Europe. But major hurdles remain for Reagan's SDI program and even for the seemingly easier goal of reducing missiles in Europe.

Nonetheless, Reagan and the Soviet leader engaged in an intense two days of personal diplomacy at Geneva unlike anything else in the president's first five years. Helmut Sonnenfeldt of the Brookings Institution, an adviser to President Nixon, said it is now an open question "whether the dialogue that these two leaders began in Geneva will be continued in a way that will make real negotiation possible."

The Geneva meeting has already paid off in one sense for Reagan. During the 1984 campaign, his advisers felt his one vulnerability was the charge by Walter F. Mondale that he would lead the nation into nuclear war. Now, polls show Reagan is getting the highest marks ever for his handling of foreign policy.

"On arms control," said pollster Richard Wirthlin, "the president next year will have strong assets perceptually he didn't have a year ago. There is no doubt in American minds that he can deal with Gorbachev effectively. That's been put to bed with Geneva. The question is: Can we use the opportunity of another meeting to advance the process?"

Reagan also will juggle some other problems next year. Foremost will be efforts to solidify the resurgent strength of the Republican Party and keep its control of the Senate. At the same time, Reagan will be pushing tax revision and the Gramm-Rudman-Hollings budget knife will begin to cut.

Pressures on the Senate could be volatile. Richard Whalen, a Washington economics consultant and author, said, "The story that will unfold in '86 is the conflict between the White House and the Republican Senate over a wide range of fiscal choices, beginning with tax revision, deficit reduction and coming inevitably to revenue enhancement," a tax increase.

According to Laxalt, general chairman of the GOP, "The Republican Party will go where the economy and Ronald Reagan goes."

Laxalt described as "still in the yeasting stage" the party realignment that many Republicans hoped would come out of the Reagan years.

The recession of Reagan's first term destroyed those hopes of a realignment, but during the last year polls show that Republicans have closed much of the gap with Democrats in party identification.

"The allegiance to the Republican Party has not only shifted," said Wirthlin, "but it is a shift that appears to be much better seated, better established. That doesn't mean we have a realignment. The last stage is in local and state elections. But it does suggest that politics will be played in 1988 on a very different chessboard than in 1984 and 1980."

Whalen said that while Republicans have improved their strength since the 1970s, "many of their gains are highly contingent, and the promise made to younger people is that we will continue noninflationary prosperity. At the first sign that promise is broken, I think these people will behave just like their parents -- and go looking for somebody else to take care of them."