RUSSIA IS pressing the United States to recognize its independence and that of Ukraine and Byelorussia, the other founding members of the Commonwealth of Independent States that is emerging as the successor to the Soviet Union.

Secretary of State James A. Baker III, touring the capitals of the republics, says that Washington will look closely at the request. Secretary of Defense Dick Cheney, however, says that he sees no reason for delay. "The reality is the old Soviet Union is dead and we've got to deal with the new mechanism."

A huge problem is that there is simply no precedent for dealing with what is befalling the vast empire assembled by the czars and their Marxist successors. The world is used to dealing with a powerful central government in Moscow, one that could be held accountable for the agreements and treaties it signed. But the new commonwealth, so its founders say, will be without a strong central executive, except when it comes to controlling nuclear weapons.

Washington has set legitimate preconditions for granting Ukraine the diplomatic recognition it first asked for weeks ago. Among them: protection of minority rights, no border changes without mutual agreement, tight controls over nuclear weapons and assumption of a fair share of the Soviet debt.

The first thing the states of the new commonwealth must do is decide among themselves what the legal basis of their relations will be, and how they will deal with the outside world. National independence raises many problems. The new states have not even begun to consider them.