The main aim of this work is the theoretical prediction and analysis of the nonlinear behavior of crystallization processes. As a first step towards the theoretical analysis a fairly simple population balance model including fines dissolution and classified product removal has been considered. By means of numerical bifurcation and stability analysis, regions in the parameter space of the operating conditions and the physical properties with periodic behavior have been predicted. Due to the simplicity of the underlying model the results are only of qualitative nature. Future work will focus on a quantitative prediction of the nonlinear behavior with more detailed models and an experimental verification.