A zero dimensional, mean-value, control-oriented model for recompression homogeneous charge compression ignition (HCCI) combustion with two discrete states representing temperature and composition dynamics is presented. This model captures steady state magnitudes and trends in combustion phasing, residual gas fraction, and mass flows caused by sweeps in valve timings, fueling rate, and fuel injection timing. It is shown that the coupling of the composition state with the mainly thermally-driven combustion dynamics causes competing slow and fast dynamics that shape the transient response of the phasing. A decoupled version of the model, where composition does not affect combustion phasing, is also developed in an effort to further simplify the model. This version matches the steady state fidelity of the coupled model, but has a qualitatively different dynamical behavior. Both models exhibit complex behaviors such as limit cycles at extremely late phasing. Both realizations are valid contenders as low order steady state representations of HCCI behavior. High-fidelity transient data will be necessary to further clarify the necessity of including composition effects on combustion phasing.