Consideration is made of a combined process of anionic polymerization and crystallization at the particulate level. The model includes the equations of the polymerization and crystallization kinetics and the heat balance equation taking heat effects of both the processes into account. The physical mechanism of the instability of steady states of the process is revealed. It is shown that both well-known types of the onset of instability break are possible : the "soft" type, when the amplitude of the new self-oscillating regime is growing monotonously from zero while crossing the neutral stability boundary, and the "hard" one, when it suddenly jumps from zero to a finite value. Characteristics of self-oscillations of temperature and polymerization degree are studied by means of bifurcation technique and numerically.