A reactor model was developed to describe the dynamics of continuous solid-phase polymerization (SPP) of nylon 6,6 in a moving bed. This partial differential equation (PDE) model was used to simulate the start-up process for a reactor filled with cold particles. Polymer property profiles (degree of polymerization and moisture content) along the reactor and inside the polymer particles are presented at different reaction times. Simulations show that approximately two solid-phase residence times are required to reach the desired steady-state conditions at the reactor outlet. After the process reached steady state, operating conditions were adjusted to move the reactor system to new steady states. Model predictions for the reactor dynamics after the step changes show how adjustments to the operating conditions affect the SPP process. Variations in the temperature, moisture content and flow rate of the counter-current nitrogen gas have important effects on the polymer properties.