In this paper, a model for two-layered video traffic is proposed. The performance analysis of the proposed model and the effects of two-layer coding scehemes in ATM networks are also studied. ATM-based networks give the possibility to support image codingat variable bit rate(VBR). Two layer coding is one of the very promising methods among many proposed methods to compensate the cell loss, the major drawback in ATM networks. From the experimental data of the 2-layer coded video traffics, it is observed that traffic patterns of base layer and enhanced layer are highly correlate to each other, when constant image quality is kept. With this observation, coded two layered video traffic can be modeled as 2-dimensional Markov chain. The model well fit the real experimental data. The model was used for the analysis of the performance of statistical multiplexer with priorites in ATM networks.