Ronald Reagan's political triumph does not diminish the national security and diplomatic problems he faces. Nor does it offer the likely prospect of being able to solve those problems with significantly greater ease.
The President says the top priorities of his second term are ''peace and disarmament,'' backed up by a continued strengthening of US military might. Yet he must deal with the same wary and sometimes truculent Kremlin leaders on arms control, men who themselves are sorting out succession difficulties.
Mr. Reagan's push to ''rearm America'' will continue to be modified by lawmakers, just as it was in the second half of his first term.
Controversial military items - the MX missile, antisatellite weapons, and space-based systems to defend against attacking warheads - will be fought over as hard as ever.
And the newly elected 99th Congress - which includes two additional Democratic senators and fewer new Republican representatives than the GOP had hoped for - is not likely to be much more disposed than its predecessor to the use of American armed force abroad. This expectation is despite the possible chairing of the Senate Foreign Relations Committee by conservative Jesse Helms (R) of North Carolina.
Still, some experts see the opportunity for Reagan to achieve progress where so far there has been little.
''The President clearly has a mandate to move assertively, and I would hope in a centrist fashion on the East-West issue most of all ... and secondly perhaps on the Middle East, though there, caution I think is to be desired,'' said Zbigniew Brzezinski.
''The present trend is for both the Arabs and the Israelis to want us more and more (to be a mediator), and I think that's a good development.''
On arms control, Dr. Brzezinski says that Reagan now ''has momentum going into the talks.... He has a strong hand, and when you have a strong hand, that's the time to deal.'' But, like many other observers, the former national-security adviser is less sure about the predisposition of the administration to act boldly in this area. ''Whether they have the internal organization and whether they have the necessary combination of process and personalities to shape an effective negotiating strategy, I do not know,'' he told the Monitor.
Soviet Foreign Minister Andrei Gromyko this week criticized the US military buildup and what he called ''state terrorism.'' But he also said, ''We are ready to cooperate ... in the interests of strengthening international security.''
There may be some possible new openings for such cooperation. It was reported this week that the two superpowers will hold talks in Moscow this month on controlling the proliferation of nuclear weapons to other countries.
In January, senior US and Soviet officials are scheduled to discuss ways to expand trade between the two countries.
Chief US arms negotiator Edward Rowny said recently that the United States is ready ''to explore with the Soviets trade-offs that we could make'' on strategic (intercontinental) nuclear weapons.
There remain, however, strong differences of opinion within the administration on just how forthcoming the US should be.
And on intermediate-range nuclear forces in Europe, the Soviet Union refuses to return to the bargaining table unless the US-built Pershing II and cruise missiles being deployed in five countries by NATO are removed.
The Belgian government this week affirmed that the deployment of cruise missiles there would begin on schedule next March if Euromissile talks are not resumed in Geneva.
In Central America, the Reagan administration - despite the election results - is not likely to win congresssional support to help the anti-Sandanista rebels in Nicaragua. Officials say speculation about a US invasion of Nicaragua ''is absurd.''
Still, there is continued concern about the possible shipment of Soviet-built MIG-21 fighters to that country, which US officials say would be ''an extreme escalation.'' Some officials have reportedly suggested that a US military response might be required.
The Reagan administration can be expected to continue developing a strategic relationship with the People's Republic of China, including more exchange visits of defense officials and the supplying of some military equipment and high technology.
The President recently warned Pakistani President Mohammed Zia Ul-Huq against that country's possible development of nuclear weapons, which could affect the economic and military aid this administration gives Pakistan.
In the wake of Indian Prime Minister Indira Gandhi's assassination, US officials will watch closely for signs that her son and political heir, Rajiv Gandhi, desires a closer relationship with the US.
The Reagan administration - and especially Secretary of State George Shultz - will continue to warn of growing ''state-sponsored terrorism,'' although retaliating for attacks against Americans abroad will remain difficult.
During his first term, President Reagan received nearly all he requested from Congress in building up the defense budget. The Pentagon plan has been to seek steep increases over several years, much of it for the procurement of new weapons.
Defense officials expect requested annual budget increases (which averaged about 10 percent the first term, not counting inflation) to drop sharply beginning in 1987. But critics fear that the ''bow wave'' of weapons procurement , particularly for such items as aircraft carriers, will require larger amounts.
Many of the administration's most severe critics on weapons procurement have been Republicans concerned with federal deficits as well as cost overruns. Those same Republicans can be expected to keep up their pressure despite the President's reelection landslide.