The article presents the results of a magnetism study in quasi-two-dimensional MAX₃ (M=Cr, A=Ge, Si and X=S, Se, Te) systems. We calculated the microscopic magnetic parameters using quantum mechanical methods and showed that MAX₃ can have a high spin polarization. The easy magnetization axis lies normal to the layer plane. The main magnetic order of the CrGeSe₃, CrGeTe₃, CrSiSe₃, and CrSiTe₃ atomic systems is ferromagnetism. CrGeS₃ and CrSiS₃ exhibit antiferromagnetism. The low energy stability of the magnetic order is confirmed by the calculated values of the exchange interaction integral (J). We showed that the magnetic order realizes only at low temperatures. A study of the dependences of J and the magnetic anisotropy energy on the structural (distance between magnetic ions, distortion of the octahedral complex) and electronic properties (population and hybridization of atomic and molecular orbitals) has been performed. The dependences indicate three possible mechanisms of the exchange interaction. We have given ways of influencing a specific mechanism for managing exchange interaction.