If by some sleight of hand it could be arranged that Konstantin Chernenko and Ronald Reagan could meet together privately and unknown to others, they could chat in easy agreement together about one thing.
They could agree about the trials and tribulations that beset a superpower in its relations with its various clients, satellites, dependencies, and feodaries. Above all, they would agree that ingratitude is a major characteristic of the behavior of the lesser states that cluster by force or choice around the knees of a superpower.
Moscow's troubles in this department are legendary. It has few satisfied clients. The sudden amnesty for hundreds of political prisoners in Poland over the past week is a symptom of a chronic problem there. The amnesty had to be granted to appease popular sentiment in Poland, but it is done at the price of putting back on the streets political activists who will probably stir up more demands for independence from Moscow and from the Soviet political system.
Washington is less accustomed to similar troubles, since its clients are voluntaries. They can all, at least in theory, opt out of the US system of alliances and associations.
This week Ronald Reagan had on his plate more than a usual quota of difficulties in his department of client management. New was the coming-to-power in New Zealand of a Labor Party committed to the exclusion from its harbors of American nuclear-armed or nuclear-powered warships. And this came on top of a season of continuing difficulties with Greece, where street demonstrations by strikers at the entrance to American military bases have become a routine, popular entertainment and impediment to traffic.
More serious in the long run is the outcome of the elections in Israel. The opinion polls and Washington had expected a solid win by the Labor Party. This would presumably have cleared the way, after the American election, for a new start at reaching a comprehensive settlement between Israel and its Arab neighbors.
The moderate Arab states, principally Jordan and Saudi Arabia, were primed for a new round of negotiations with a new government in Israel committed to the idea of exchanging occupied territory for peace.
But the votes did not give the Labor Party the expected victory. Instead, it left Labor and the pro-annexation Likud party nearly even, surrounded by fragments of lesser parties. A weak and unstable coalition government is apparently the only way out. A comprehensive peace in the Middle East is left as remote as ever.
Then there is Central America, where the military in Honduras is becoming restless and unhappy about the country being used as a base for United States military maneuvers and American-backed guerrilla operations against Nicaragua. The schedule for more US maneuvers in Honduras this summer has been trimmed back. Several Nicaraguan guerrilla leaders have been denied reentry permits.
It is not clear yet whether the new Honduran military leaders, who strongly influence the civilian presidency, merely want to be paid more for the use of their territory by the US. Perhaps a larger subsidy to Honduras would overcome the new reluctance. But there is also the factor of local nationalism. Superpowers seem often to be surprised at how unpopular their troops can become in the cities and villages of a client state.
No one outside the high command in Washington knows whether President Reagan is thinking in terms of an American invasion of Nicaragua from Honduras after the November elections are out of the way. But if there is such an idea, its chances are declining. Congress is more than ever opposed to funding the ''contras.'' And now we have rising Honduran opposition to US, or US-backed, military operations on its territory.
Among these new problems the New Zealand question is probably the most easily manageable. US Secretary of State George Shultz has been in friendly conversation with the new leaders of the New Zealand Labor Party. Those leaders do not want to risk leaving the existing ANZUS alliance with Australia and the US, no matter how vociferously anti-American some of their left-wing followers may be.
The chances are that the difficulty will be overcome by the expediency of finding it unnecessary to have American warships carrying nuclear weapons in New Zealand ports until the present excitement blows over.
Keeping Greece happy and inside the alliance is more difficult because of the friction that continues between Greece and Turkey. Troubles around the American bases in Greece itself would probably subside if Washington would require the Turks to give up some of those portions of Cyprus that were Greek until the Turkish invasion in 1974.
But Washington could not satisfy the Greeks about the partitioning of Cyprus without offending the Turks. Turkey is the eastern military anchor of the Atlantic alliance and is considered to be essential to the successful defense of the southern flank of NATO.
There is no formal department in the government in Washington for the management of relations with client states. If there were such an office it would be easier for everyone to follow the story of those relations.
The word empire is currently in disrepute. No one in high places in Washington would admit that there is such a thing as an American empire.
Yet the interlocking system of associations and alliances that revolves around Washington is similar in substance to the system that once revolved around the Palace of Westminster in London and was known as the British Empire.
The head of the British Colonial Office back in the heyday of the British Empire would understand President Reagan's current problems with New Zealand, Greece, Israel, and Honduras.
There is no visible prospect of an early exchange of notes between Messrs. Reagan and Chernenko about such matters. But, in fact, they have similar problems in managing their very different imperial-type systems.