Computer and communication network of the future will be the ISDN that enable various services. And now, it Is very Important to study the relevalent techniques to develop Interworking methods between existing computer network and ISDN The purpose of this paper Is to provide necessary basic He search results on the Interworkting method between local area network (LAN) and ISDN. For Interworking, we analyze the characteristic of existing LAN and ISDN and discuss considerations of Interworking and suggest the interworking method for CO and CL services. Also. we construct logical gateway for Interworking betwen LAN and ISDN and make formairnodeling of gateway using Petri net and verify the correctness of protocol with reachability tree. Research results should be helpful In designing and Implementing gateway between i()cal computer network and I SDN