The Integrated Services Digital Network(ISDN) is under re-design to provide flexibility which will ensure efficient network utilisation in the provision of broadband services. The main broadband services envisaged for provision on the Broadband ISDN(B-ISDN) are : Videophone; Videoconferencing; Television and High Definition TV. The B-ISDN will be a packet switched network where the packets(cells) will be transferred by the Asynchronous Transfer Mode(ATM) concept. Unlike voice and data services, the impact video services will have on the BISDN is unknown and hence loss of information is difficult to predict. Present videophone terminals are based on the CCITT H.261 Video Coding standard hence the picture quality is variable because video codec traffic is transmitted at a constant rate. To maintain a constant quality picture the codec output data must be transmitted at a variable rate or alternatively, for constant rate video codecs extra information must be made available to achieve constant picture quality. This latter technique is 2- Layer video coding where the first layer transmits at a constant rate and the second layer at a variable rate. The ATM B-ISDN promises constant picture quality video services, therefore to achieve this aim the impact variable rate video sources will have on the network must be determined by network simulation, thus variable rate video source models must be derived. To statistically characterise and stochastically model 1-Layer VBR(Variable Bit Rate) H.261 Video Codec traffic, here a videophone sequence is analysed by two alternative strategies : Talk-Listen and Motion Level. This analysis also found that 2-Layer H.261 Video Codec traffic can be stochastically modelled via a 1-Layer VBR H.261 Video Codec traffic model. Numerous hierarchical stochastic models with the ability to capture the statistical characteristics of long video sequences, in particular the short-term and long-term autocorrelations, are presented. One such model was simulated and the resulting simulated traffic was analysed to confirm the advantage hierarchical stochastic models have over non-hierarchical stochastic models in modelling video source traffic.