Traditionally, internal combustion engines follow thermodynamic cycles comprising a fixed number of crank revolutions, in order to accommodate compression of the incoming air as well as expansion of the combustion products. With the advent of computer-controlled valve trains, we now have the possibility of detaching compression from expansion events, thus achieving an "adaptive cycle" molded to the performance required of the engine at any given time. The adaptive cycle engine differs from split-cycle engines in that all phases of the cycle take place within the same cylinder, so that in an extreme case the gas contained in all cylinders can be undergoing expansion events, resulting in a large increase in power density over the conventional 4-stroke and 2-stroke cycles. Key to the adaptive cycle is the addition of a variable-timing "transfer" valve to each cylinder, plus a space for air storage between compression and expansion events. If the air-storing space has sufficient capacity, it also has an energy-storage effect similar to that of batteries in a hybrid power train. The paper presents a time-dependent simulation of the adaptive-cycle engine as a function of parameters such as maximum compression pressure, transfer valve timing, and number of expansions for each compression event. The simulation is a new code that integrates conservation equations within the cylinder and the air storage tank, including temperature-dependent properties plus heat transfer, friction, and knock onset models. Results of the code were calibrated against GT-Power simulations, for lack of any existing experimental data. The results show the following among other things: 1. The most efficient mode of operation in steady-state usually comprises two expansion strokes for each compression stroke. 2. A relative improvement in fuel economy of nearly 20% over the 4-stroke cycle is readily achievable. 3. The potential exists for a tenfold increase in power density over the 4-stroke cycle, for a length of time controlled by the capacity of the air-storage tank. 4. This can be achieved without danger of engine knock, using fuels of low octane rating.