The generalized network problem and the closely related restricted dyadic problem occur frequently in applications of linear programming. Although they are next in order of computational complexity after pure network or distribution problems, the jump in degree of difficulty is such that, in the most general problem, there exist no algorithms comparable in speed to those for pure networks. In this paper we characterize the properties of a special class of generalized network problems that permit a dual feasible basic solution to be determined in one “pass” through the network. In particular, this class includes the class of pure network problems for which no such procedure has previously existed. Our algorithm also makes it possible to apply Lemke's dual method and the poly-ω technique of Charnes and Cooper in an efficient manner to solve capacitated (pure) network problems.