The recent progress of B-ISDN signaling systems has enabled networks to handle calls which require a wide variety of ATM connection sets. This paper is concerned with the circuit group which handles calls requesting asymmetric forward and backward multi-connections, and has the capability of both bandwidth negotiation and bandwidth reservation as a traffic control for enhancing call blocking performance. A model of the circuit group is first established focusing on the call level characteristics of the group, and then a method based on the reduced load approximation and an approximate analysis of a multirate group is proposed for calculating approximate blocking probabilities. The accuracy of the approximation method is evaluated numerically by comparing with an exact method and simulation. Further the impact of bandwidth negotiation and reservation on call blockings is examined based on numerical examples.