The CL network fer CBDS(Connectionless Broadband Data Service) defined by ITU-(International Telecommunication Union-Telecommunication) consists of CL(ConnectionLess) servers which route frames and links which connect between CL user and CL server or between CL servers[1][2]. In this configuration, two kinds of congestion, CL link congestion and CL server congestion may occur. Therefore this paper has proposed the scheme that can deal with the above congestion state of LAN traffic efficiently in interworking LANs in ATM network. Proposed schemes ale link-by-link scheme and hybrid scheme. Link-by-link scheme uses the ABR feedback loops of AIM layer between CL user and CL server or between CL servers, and the header translation table carrying out the routing function of frame. And hybrid scheme is the scheme that adds end-to-end loop to link-by-link scheme and then uses RM message using CLNAP-PDU(ConnectionLess Network Access Protocol - Protocol Data Units) of CL layer. These schemes can be implemented easily because of using the ABR loop of ATM layer, end-to-end loop of CL layer, and the routing function of CL server. In this paper the characteristic and effects of two schemes in CL server bas been compared and analyzed.