Inspired by an increasing interest in multicriteria 0-1 programming problems in general and by a recent result on the reducibility of minimax to minisum problems in particular, we consider properties of efficient and optimal solutions to two-criteria (minisum and minimax) 0-1 programming problems with any constraint set. A solution procedure is suggested for solving problems whose objective functions are a convex combination of these criteria. The solution properties are illustrated with examples mainly within the context of locational decision problems.