PRESIDENT Bush's announcement of deep cuts in the nuclear arsenal of the United States was a radical and welcome response to the quick transformation of super-power relationships since the failed August coup in Moscow.Military competition between the Soviet Union and the US, on the wane throughout Mikhail Gorbachev's tenure at the Kremlin, has now evaporated. Today's decisions are driven by the onset of republic-based Soviet politics and the need to cooperate in eliminating the burden, and danger, of nuclear forces. Declaring that the US should lead the way toward an era of cooperation, Mr. Bush proposed the removal of all American tactical nuclear weapons from Europe and from warships. He also announced plans to push toward the elimination of land-based strategic missiles that carry multiple warheads. Nuclear-tipped missiles covered by the START agreement and strategic bombers have already been taken off alert. The immediate Soviet response has been enthusiastic - not surprising, since some of these steps had previously been urged by Moscow. In line with political realities, Bush called Boris Yeltsin as well as Mr. Gorbachev last Friday to let them know of his plans. American arms experts are on their way to Moscow to more fully explain the US initiative to Soviet and Russian leaders. One purpose of the president's move is to prod those leaders to deal immediately with the problem of controlling their far-flung nuclear arsenal. A sweeping reduction of short-range tactical, or battlefield, weapons would be a logical beginning, since these are the most likely to fall into the wrong hands. Another rationale for the Bush proposal is the nature of the security threat posed by a rapidly changing world. Regional strife is being ignited by ethnic friction and economic inequity, not by the old East-West ideological confrontation. Highly mobile peacekeeping troops will be more in demand than NATO-type armored units. In this vein, too, arms control will have to move beyond big-power nuclear disarmament to constraints on the transfer of conventional high-tech weaponry. The president did himself no harm politically with his arms reduction announcement either. It showed good sense and flexibility.