This work describes the mathematical modeling of the thermal decomposition of the complex compound [Ni(En)₃](ClO₄)₂ (En = C₂H₈N₂ = ethylenediamine) in an inert atmosphere under non-isothermal conditions. This process is characterized by several simultaneous and intense stages: elimination of ethylenediamine from the nickel coordination sphere, decomposition of perchlorate anions, and explosive-like oxidation of free or bound ethylenediamine. These stages overlap and merge into a one step on the differential thermogravimetric curve. Typically, this curve is modeled as a one-stage process during kinetic analysis. In this paper, for the first time, the data from the dynamic mass-spectral thermal analysis and thermogravimetric analysis were modeled using the hybrid genetic algorithm, and the results were compared. A two-stage scheme of [Ni(En)₃](ClO₄)₂ thermolysis was proposed and the kinetic parameters for each stage were obtained. It was shown that the decomposition of [Ni(En)₃](ClO₄)₂ begins with the elimination of one molecule of ethylenediamine (stage A), then the perchlorate anions quickly decompose with the evolution of oxygen (stage B). We believe that the resulting ClO4−x− (x = 1–3), as stronger oxidizing agents, instantly start an explosive-like exothermic process of ethylenediamine oxidation (stage B).