In the transmission process of a video signal over ATM networks, cells are inevitably exposed to delays, errors and losses due to the statistical multiplexing used in these networks. These phenomena affect the quality of the video signal and without adequate measures to control the propagation of the impairments the quality of the service may fall below acceptable levels. In the first part of this paper, we present an Adaptive Data Partitioning (ADP) Scheme. This scheme splits a video stream into a high priority and low priority substreams. In the second part of the paper, we propose a novel hierarchical packing scheme for the transmission of the two video substreams over ATM. The proposed packing scheme overcomes the problem that when no provisions are taking to properly pack a hierarchical-encoded video stream, the loss of a high priority ATM cell will result in the complete loss of the group of cells. Results for different video sequences and different bitstream split levels are given, showing the efficiency of our schemes.