The mathematical theory of differential games is used to study the structure of optimal allocation strategies for some time-sequential combat games with combat described by Lanchester-type equations of warfare. As required by such applications, some new theoretical results are given: first order necessary conditions of optimality are developed for differential games with state variable inequality constraints. These results are used to study optimal air-war strategies in a differential game model. In a different model, optimal air-war strategies are further studied within the context of land-war objectives. Optimal fire-support strategies are studied in an attack scenario with a differential game model. A comprehensive survey of previous literature on each of the above topics is given. Finally, some problems for possible future study are discussed. (Author)