A theory of auroral substorm dynamics is constructed on the basis of MHD wave processes in the ionosphere-magnetosphere system. The basic view is that the substorm commences in the nightside near-Earth magnetosphere through a collapse of plasma equilibrium. The collapse releases a significant amount of free energy embedded initially in a collection of compressional waves. It is suggested that substorm dynamics after the collapse are determined by the evolution of these waves. We first investigate the quantitative ramifications of the waves in a two-dimensional box in the GSM yz cross section of the magnetotail. The model is constructed to allow the study of radiation of substorm wave energy into the solar wind and also encompasses the essential elements of resonant interaction in the plasma sheet boundary layer. The natural boundary condition leading to radiative loss is introduced. It is found that wave radiation into the solar wind can relax the magnetospheric system in less than a hour. The resonant Alfv¿n models driven by the normal compressional modes in the box are studied through the construction of proper dispersion equation. By studying the field-aligned current generated by resonances, we establish the auroral pattern expected to result from the coupling. Following the theoretical study, we examine an auroral substorm observed by the CANOPUS photometer array on February 20, 1990. It is found that, among the testable theoretical predictions, there exists a general agreement with the observations. We did find, however, that electron- and proton-induced aurora oscillate essentially in phase, thus implying a more complicated precipitation process. ¿ American Geophysical Union 1995