This paper is devoted to the study of operating modes of the crystallizer with allowance for the processes of nucleation and evolution of particles, removal of product crystals, and fines dissolution. The stationary and non-stationary analytical solutions describing various crystallization scenarios are derived. We show that the unsteady-state distributions of crystals approach their stationary distribution over time. In addition, the linear analysis of dynamic instability shows that the regions of oscillatory instability and absolute stability exist. These regions are divided by the neutral stability curve dependent of the physical parameters of crystallization process. We show that the oscillatory instability domain becomes wider when increasing the nucleation and growth rate constants. As a result, the process of volumetric crystallization under consideration can operate in a mode of self-oscillations sustained by a feedback between the nucleation rate and the process driving force (supersaturation). © 2023, The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.