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A new approach to the study of stochastic Lanchester processes based on diffusion approximations is presented. The distribution of the two force levels over time is shown to be well approximated by a nonstationary bivariate Gaussian diffusion process with specified mean and covariance structure. The approximation is based on an asymptotic analysis which assumes the initial force levels are large. Numerical studies are presented, however, which show surprising accuracy for force levels as small as 30. A wide variety of attrition structures are discussed including the linear and square law cases, Helmbold's general attrition structure, Karr's engagement model, and heterogeneous models. The development of tractable mathematical expressions for the time evolution of complicated Lanchester-type attrition processes makes possible the introduction and analysis of decision theoretic aspects to the problem such as force level decisions, combat tactics, reinforcement decisions, and the value of information about the opponent's strengths, weaknesses, and strategies. (Author)