The nonlinear periodic, quasi-periodic, and chaotic dynamics of a two-phase flow system are studied. The system comprises a vertical channel, heated through its side walls, into which a subcooled liquid enters at the bottom and a two-phase vapor-liquid mixture exits from the top. The system, which is driven by three time-dependent forcing functions (the variable inlet enthalpy, sidewall heat flux, and channel pressure drop), is studied as a nonautonomous nonlinear dynamical system. The numerical scheme used is developed by integrating some of the partial differential equations, first along their characteristics and then along the channel length. The resulting nonlinear functional differential equations are then solved using a special-purpose second-order numerical scheme that treats the complicated nonlinear multiple delay integrals that arise. The results of the numerical simulations and the subsequent analyses show that the nonlinear dyanamics of a nonautonomous heated channel are quite complicated and that this simple system can exhibit periodic, quasi-periodic, and quite frequently chaotic density wave oscillations.