It is considering that generally the technology strategy of the MNE (Multinational Enterprise) is "Technology Development Strategy" such as marketing and R&D. But, originally that technology strategy is a general term of "Technology Development Strategy" and "Technology Control Strategy", and we specially tend to forget the latter's existence. Then, the flow of the technology strategy of the U.S. MNE can be explained as a circulation phenomenon of that two-technology strategy historically. For example, the technology strategy of the U.S. MNE was "Technology Control Strategy (Global Patent Strategy)" from the 1960's to 1970. In those days, the U.S. MNE had worldwide technological predominance, and it was the purpose of being important to appropriate fully the returns that could be earned from the development technology. The technology strategy of the U.S. MNE changed from "Technology Control Strategy" to "Technology Development Strategy (Global R&D Strategy)" from the 1970's to 1980. In those days, the technological predominance of the U.S. MNE collapsed because a new MNE in Japan and West Germany (those days) began to gain power. For that reason, the U.S. MNE had to develop a new technology in a new method. Then, "Technology Control Strategy" is restored from the 1980's to 1990. The U.S. MNE began to aim at appropriating new development technology again because it succeeded in development of software and information technology (IT). In this paper, the flow of the technological strategy of this U.S. MNE can be named "Technology Strategy Cycle". And, the U.S. MNE had this initiative of "Technology Strategy Cycle" all the time. For example, "Technology Strategy Cycle" of the U.S. MNE keeps being followed by a new MNE in Japan and Asia as it is. In the practical use side, it is said that "Technology Hegemony" of the U.S. MNE is going on at present, too.