In this thesis, various aspects of statistical multiplexing of data and speech signals have been investigated. In the first half, a queueing model with finite waiting room and batch Poission arrivals is studied assuming that data or digitized speech signals are transmitted at a constant rate. Using traffic intensity and average burst length as parameters, the relationship between buffer size, overflowprobabilities and expected queueing delay due to buffering is obtained. To examine the performance of the system, computer simulation has been done at various conditions. The results obtained can be used in designing a buffer efficiently. In the second half, we investigate the use of a variable rate coding concept and a dynamic buffer control method for a multiple user hybrid companding delta modulation (HCDM) system. A dynamic buffer control method that gives good performance in controlling the buffer status and in adapting to the change of buffer size is proposed. By computer simulation, we have examined the performance gain of the multi-user system obtainable by sharing a channel with many users, and studied the advantages of using the proposed dynamic buffer control. It has been found that using both the variable rate coding concept and the dynamic buffer control scheme, a large amount of bandwidth compression can be achieved while maintaining good quality of speech.