MPEG compressed video is very sensitive to data loss; not only may corruption caused by the loss of an ATM cell be quite severe, but the use of inter-frame predictive coding may cause the corruption to persist or even spread over a period of several frames. In order to lessen the impact of cell loss on compressed video, several people (for example; Ghanbari, Kishino et al.) have proposed techniques for splitting the coded bitstream into two layers of differing importance to the decoded video quality, and transmitting these layer at different cell loss priorities by utilising the ATM cell loss priority bit. The great improvements gained from the use of such layered coding and transmission schemes raise the question of how much further improvement might be gained if we had more ATM cell priority levels to use. This thesis presents an investigation into the performance benefits of MPEG video transmission over a hypothetical ATM network supporting four, as opposed to the standard two, priority levels. The investigation considers three prioritisation schemes: a simple un-layered method that prioritises cells based upon the estimated level or corruption within the decoded video that may occur as a result of losing each cell, a two layer coding scheme based upon the MPEG-2 data partitioning method, and an extension of the two layer scheme to use three layers. The performance for each of these coding and prioritisation methods is evaluated in terms of the decoded root mean square error (RMSE), by transmission over a simulated one, two and four priority level ATM network. The results appear to indicate that while prioritisation of an un-layered MPEG video cell stream using two priority levels is of some benefit, extending the scheme to utilise four priority levels is of only limited effectiveness. The layered coding results meanwhile show that the new low priority layers created by extending data partitioning beyond two layer coding are not of significantly different importance to the decoded RMSE video quality to warrant transmission at different priorities, and that for the systems tested, four priority levels would again offer only a modest improvement in performance over two priority levels. Subjective video quality evaluation tests however confirm a definite difference in subjective importance between the layers, and suggest a performance improvement for four priority level transmission.