In ATM Networks, real time VBR traffic, which is inherently bursty in nature, requires dynamic bandwidth allocation. There are algorithms proposed in the literature where the bandwidth is allocated in linear proportion to the requirements. But, these algorithms lead to unequal growth in the queue size and reduction in the network performance. Minmax algorithm is one such algorithm which maintains a fair distribution of buffer lengths across the sources of a class, and performs better for homogeneous sources when compared to other dynamic allocation schemes. Nevertheless, this algorithm can be applied only when the sources demand same QoS parameter. To overcome such an inadequacy, we propose a novel method of dynamic bandwidth allocation, viz., Modified Minmax Algorithm (MMA), for multiple QoS sources. Unlike other models, MMA takes cell loss ratio (CLR) also into account besides the buffer occupancies and arrival rates. The performance of MMA has been evaluated using multiple QoS sources simulated for this purpose. The results are encouraging, for it gives better QoS performance (by an order of one) for hetrogeneous sources with different QoS values. Results on the evaluation of the performance of delay and jitter for various buffer sizes are also presented in this paper.