This paper presents a technique to determine prime implicants in multi-level combinational networks. The method is based on a graph representation of Boolean functions called AND/OR reasoning graphs. This representation follows from a search strategy to solve the satisfiability problem that is radically different from conventional search for this purpose (such as exhaustive simulation, backtracking, BDDs). The paper shows how to build AND/OR reasoning graphs for arbitrary combinational circuits and proves basic theoretical properties of the graphs. It will be demonstrated that AND/OR reasoning graphs allow us to naturally extend basic notions of two-level switching circuit theory to multi-level circuits. In particular, the notions of prime implicants and permissible prime implicants are defined for multi-level circuits and it is proved that AND/OR reasoning graphs represent all these implicants. Experimental results are shown for PLA factorization.