Different compositions of the $In_x(Se_{75}Te_{25})_{100-x}$ ($0 \le x \le 10$ at.%) chalcogenide system were prepared by the usual melt quench technique. The results of the Differential Scanning Calorimeter (DSC) under non-isothermal conditions were reported in order to study the effect of replacement of In atoms by Se or Te atoms on the glass transition, crystallization kinetics and the thermal stability for $In_x(Se_{75}Te_{25})_{100-x}$ glasses. The glass transition temperature was found to increase with the increase in In content. The thermal stability of the studied glasses has been evaluated using various thermal stability criteria ($\Delta T$, $H_g$ and $S$), based on the characteristic temperatures such as the glass transition temperature ($T_g$), the temperature at which crystallization begins ($T_c$), the temperature corresponding to the maximum crystallization rate ($T_p$). A comparison of various simple quantitative methods to assess the level of stability for $In_x(Se_{75}Te_{25})_{100-x}$ ($0 \le x \le 10$ at.%) glasses is presented. The obtained results were discussed in terms of the glass density, molar volume, compactness and chemical bond approach.