Abstract  The problem of fault detection in general combinational circuits is NP-complete. The only previous result on identifying easily testable circuits is due to Fujiwara who gave a polynomial time algorithm for detecting any single stuck fault inK-bounded circuits. Such circuits may only contain logic blocks with no more thanK input lines and the blocks are so connected that there is no reconvergent fanout among them. We introduce a new class of combinational circuits called the (k, K)-circuits and present a polynomial time algorithm to detect any single or multiple stuck fault in such circuits. We represent the circuit as an undirected graphG with a vertex for each gate and an edge between a pair of vertices whenever the corresponding gates have a connection. For a (k, K)-circuit,G is a subgraph of ak-tree, which, by definition, cannot have a clique of size greater thank+1. Basically, this is a restriction on gate interconnections rather than on the function of gates comprising the circuit. The (k, K)-circuits are a generalization of Fujiwara''sK-bounded circuits. Using the bidirectional neural network model of the circuit and the energy function minimization formulation of the fault detection problem, we present a test generation algorithm for single and multiple faults in (k, K)-circuits. This polynomial time aggorithm minimizes the energy function by recursively eliminating the variables.