Current monitoring is a well-established technique for detecting stuck-on and bridging faults in CMOS logic circuits. When such faults are activated by an appropriate vector, the circuit draws current which is much larger than normal and the fault is detected. The authors first show that any test set, which detects all single stuck-at faults in any irredundant combinational CMOS logic circuit, also detects all multiple stuck-on faults in it using current monitoring. If the constituent gates of the circuit are all primitive CMOS gates (NAND, NOR, NOT) then the authors show that the test set detects all multiple stuck-on and input bridging faults (even if the two types of faults occur simultaneously) with current monitoring. Even when the CMOS circuit is redundant the authors have found that in most cases a test set that detects all detectable single stuck-at faults also has a very high coverage for the multiple stuck-on and input bridging faults and their combinations.