This paper considers a wide class of shortest path problems in acyclic digraphs, where path lengths are given by the multiplicatively additive value. The problems are solved through bynamic programming, [4]. The bynamic programming formulation for the class has a system of two interrelated recursive equations. By solving the system, simultaneously both shortest and longest path lengths can be found. Two types of sequences which converge to the solution are proposed. By use of a directed network, two actual examples of finding both shortest and longest paths are illustrated.