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We develop some two-person zero-sum game formulations of search and evasion problems. By employing a game theoretic approach, we allow the hider, as well as the searcher, to choose a strategy. This is in contrast to most search models which assume a stationary or passive hider. Both non-sequential.and sequential search games are investigated. Some interesting aspects of the non- sequential game and an example of an antisubmarine search problem are given. The sequential games con-sist of a sequence of moves. When the players move, they not only de-termine a payoff but also the probability that the game terminates before the next move. When at most a finite number of moves is allowed, we prove that a solution may be found by solving a recursive sequence of matrix games. When the number of moves is not bounded, the game is characterized by a special type of non-linear program. The solution to this program can be approximated by successive perturbations of