This paper considers VBR transmission of multiple real-time videos over ATM networks. Multiple real-time VBR video sources are multiplexed into an ATM switch to transmit cells into the network. Given the ATM switch capacity, the problem is to dynamically allocate the required channel bandwidth for each video source such that the encoder buffer occupancy is maintained at a target level. To solve the problem, we present a mathematical formulation and propose an algorithm for the bandwidth allocation. To allocate a suitable bandwidth at a given control period, QoS demand levels and traffic characteristics of the video sources are considered. The performance of the proposed scheme is examined in terms of the number of encoder rate controls required and the gap between the target and the current buffer occupancy at each control period. Numerical results are analyzed for different QoS environments as well as different levels of target buffer, ATM switch capacity, buffer size and leaky bucket token rate.