Autoignition histories are considered under conditions such that the compression and heat release occur sufficiently rapidly that molecular transport is negligible during the ignition and propagation processes. The objective is to account for arbitrary spatial variations of temperature and composition that may be present when ignition begins. A one-step, Arrhenius reaction of large activation energy and arbitrary orders with respect to both fuel and oxidizer describes the.chemistry. Expressions are obtained for the ignition time and for the rate of pressure buildup after ignition in terms of the temperature and species concentrations that exist in the nonreacting, multiphase, turbulent flow just prior to or shortly after ignition