This thesis presents a theory to help military leaders determine the best time to conduct a hostage rescue attempt. The theory is based on the phenomenon of a hostage crisis "biorhythm." According to the theory, there are four principles essential for hostage rescue mission success: surprise, intelligence, operator's skill, and deception. These principles are derived from planning models used in special operations, personal experience, and an analysis of six historical case studies. The case studies show that if any one of these four principles was overlooked, the operation was doomed. The principles have been determined to be the most critical factors that change as a hostage crisis develops. The focus of this thesis is an in-depth case study of the hostage rescue operation Chavin de Huantar in Lima, Peru. This case study presents compelling evidence to reinforce the author's hypothesis, and serves as a model for successful rescue operations. Another focus of this thesis is the use of game theory analysis during a hostage crisis. The findings of the thesis will help decision makers plan and organize hostage rescue forces to act at the appropriate time, maximizing their chances of success. In addition, it will provide a useful planning model that can be implemented effectively and accurately, presenting a clear picture of possible outcomes throughout a hostage crisis. It is hoped that this thesis will help the reader become a better strategist during the planning, preparation, and execution of a hostage rescue operation. The other case studies that are analyzed according to the biorhythm theory are Operation Eagle Claw, launched to rescue the Iran hostages in Tehran in April 1980; the De Punt train hijacking in Holland in May-June 1977; the Munich Olympics Massacre in West Germany in Sep 1972; Egypt Air Flight 648 at Malta in Nov 1978; and Operation Fire Magic, Lufthansa Flight 181, Mogadishu, Somalia in Oct 1977. (45 figures, 141 refs.)