In this paper two problems of the nuclear strategy and its movement in the United states are treated. (1) Since the late 1960's the debates on nuclear strategy have been deployed in the United States. In this dispute, the crucial point was how to deal with the situation of the mutual nuclear invulnerability between the U.S. and Soviet Union. There seem to be two standpoints : the so-called 'dove' group ('stable balancers') and 'hawk' group ('war fighters'). Distinguishing the chracteristics of the two groups, the following five aspects are investigated and evaluated in this paper, i. e., (1) the evaluation of the nuclear weapons as a means of the war (2) the strategic meanings of winning the nuclear war (3) the evaluation of the reinforcements of the Soviet nuclear capability and threats (4) the capability of the mutual assured destruction (MAD) (5) the arms control. (2) Today, it causes pulic discussion that the policy of the limited nuclear options has been promoted by the Reagan Administration. But the policy had not been firstly taken up by President Reagan. In the process of the strategic debate, the Nixon, Ford and Carter Administrations had inclined to the 'hawk' side, such as the 'targeting doctrine' of Nixon Adminstration and 'countervailing strategy' of Carter's. Reagan has just followed and strengthened the policy of former adminstrations.