The crystallisation kinetics of bulk $Se_{85-x}Te_{15}S_x$ (x = 5, 10, 15, 20 and 25 at. %) ternary-component chalcogenide glasses have been studied using differential scanning calorimetry with different heating rates ($eta = 5, 10, 20, 30, 40$ K/min). The studied alloy exhibited overlapping exothermic peaks which were deconvoluted using a Gaussian fitting of two peaks, making it possible to study the crystallization phases separately. The glass transition activation energy $E_g$ and the crystallization activation energies for the first and the second crystallization peaks ($E_{c1}$ and $E_{c2}$) have been identified. The determined kinetic parameters have made it possible to postulate the type of crystal growth exhibited in the crystallization process. The phases at which the alloy crystallizes after the thermal process have been identified by X-ray diffraction. The diffractogram of the transformed material indicates the presence of microcrystallites of $Se_{7.68}Te_{0.32}$ and $S_5Se_4$, with a remaining additional amorphous matrix.