A thorough algebraic analysis of multiple fault situations in combinational logic networks is developed, using the concept of boolean difference. Boolean difference has been widely used as a mathematical tool to generate test sets for single faults in combinational networks. In this paper the concept has been extended to encompass all possible multiple faults. Compact expressions have been developed for complete test sets of a specifick-fault as well as for all possiblek-faults for any value ofk. Several interesting special situations have been discussed where boolean-difference expressions are reduced to a much simpler form for computation.