This paper describes a theoretical analysis of highly cooled attached and separated regions of shock wave-laminar boundary-layer interaction in the presence of strong streamwise pressure gradients generated by boundary-layer displacement effects at the leading edge. This method is an extension of an earlier analysis by Holden1'12 to conditions where the inviscid flow cannot be described by simple isentropic flow relationships, and where the boundarylayer upstream of the main interaction is subjected to a strong pressure gradient. The analysis is compared with measurements described in Part II of the study. For strong leading edge displacement effects (%z, > 1), the analysis predicts that highly cooled boundary layers in hypersonic flow will be supercritical; a supercritical-subcritical jump is therefore required to join the solution to the subcritical viscous layer at separation. An examination of the experimental measurements indicates that the supercritical-subcritical jump does not reflect a sudden and basic change in the flow mechanics of separation, but is an approximation necessary because the conventional boundary-layer equations cannot adequately describe the viscous interaction process leading to separation. For some high Mach number, low Reynolds number conditions, we were unable to obtain a unique solution, without recourse to experimental data, by locating a critical point in the throat region of the flow. As in the separated region, there is serious question whether the conventional boundary-layer equations can be used to adequately describe the mechanism of boundary-layer reattachment in these flows.