A rapid-compression machine is a laboratory apparatus to study aspects of the compression stroke, combustion event, and expansion stroke of an Otto cycle engine. As a simple model of such a machine, unsteady onedimensional nonisobaric laminar flame propagation through a combustible premixture, enclosed in a variable volume, is examined in the asymptotic limit of an Arrhenius activation temperature large relative to the conventional adiabatic flame temperature. In this limit, a thin propagating flame separates the nondiffusive expanses of the burned and unburned gases. The pressure through the enclosure is spatially homogeneous for smooth flame propagation. However, expansion of the hot burned gas results in compressional preheating of the remaining unburned gas and, in fact, the spatially homogeneous gas may undergo autoconversion prior to the arrival of the propagating flame. If such an explosion is too rapid for acoustic adjustment, large spatial differences in pressure arise and the resulting nonlinear waves produce audible knock. Here, attention is concentrated on what fraction (if any) of the total charge may undergo autoconversion for a given operating condition and what enhanced heat transfer from the end gas would preclude autoconversion-although too great a heat transfer from the end gas could result in flame quenching (unburned residual fuel).