Connectionless service for LANs interconnection will be provided in ATM networks at an early stage of B-ISDN era. This service will be provided on connection oriented mode at ATM technology. To perform this service, ATM connections using the dedicated bandwidth for this service are established semi-permanently between the nodes accommodating LANs. On these ATM connections, connectionless service among LANs is provided. It is important for private networks to utilize this bandwidth efficiently for reducing communication cost. In this paper, the architecture to provide connectionless service in private networks is described. Next, the allocation schemes of the bandwidth for this service and their performance are considered. We discuss the following schemes and compare them. One scheme is to establish semi-permanent ATM connections between the nodes with LAN interfaces. The bandwidth for each connection is individually assigned between these nodes. In another scheme, CLSFs (Connection-Less Service Functions) are introduced for connectionless service and connections are established via CLSFs. We show the latter scheme is superior because it brings out the effectiveness of statistical multiplexing of ATM technology and it leads to the reduction of the allocated bandwidth.