In the near future, multimedia will form the majority of Internet traffic and the most popular standard used to transport and view video is MPEG. The MPEG media content data is in the form of a time-series representing frame/VOP sizes. This time-series is extremely noisy and analysis shows that it has very long-range time dependency making it even harder to predict than any typical time-series. This work is an effort to develop multi-step-ahead predictors for the moving averages of frame/VOP sizes in MPEG-coded video streams. In this work, both linear and non-linear system identification tools are used to solve the prediction problem, and their performance is compared. Linear modeling is done using Auto-Regressive Exogenous (ARX) models and for non linear modeling, Artificial Neural Networks (ANN) are employed. The different ANN architectures used in this work are Feed-forward Multi-Layer Perceptron (FMLP) and Recurrent Multi-Layer Perceptron (RMLP). Recent researches by Adas (October 1998), Yoo (March 2002) and Bhattacharya et al. (August 2003) have shown that the multi-step-ahead prediction of individual frames is very inaccurate. Therefore, for this work, we predict the moving average of the frame/VOP sizes instead of individual frame/VOPs. Several multi-step-ahead predictors are developed using the aforementioned linear and non-linear tools for two/four/six/ten-step-ahead predictions of the moving average of the frame/VOP size time-series of MPEG coded video source traffic. The capability to predict future frame/VOP sizes and hence the bit rates will enable more effective bandwidth allocation mechanism, assisting in the development of advanced source control schemes needed to control multimedia traffic over wide area networks, such as the Internet.