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Nondeterministic differential games of imperfect information are considered, with particular emphasis on the case of a linear system, a quadratic cost functional, and independent white Gaussian noises additively corrupting the observable output measurements. Solutions are presented for a number of particular cases of this problem, including those in which one of the two controllers has either no information or, under certain additional restrictions, perfect measurements of the state vector. In each case the optimal control for each controller is shown to be closely related to that which would result by assuming a separation theorem to hold. Furthermore, the various terms in the resulting optimal cost are shown to be readily assignable to the appropriate contributing source, such as the optimal cost that would result if the problem were instead a deterministic one with perfect information, the effect of estimation errors, or the effect of measurement errors.