The matrix of multicomponent diffusion coefficients plays a fundamental role in the method of determining mass transfer coefficients in multicomponent systems. This matrix however has to fulfill strictly defined conditions in order to be applied in the method mentioned above; their eigenvalues must be real and positive. Basing on the principles of irreversible thermodynamics as well as using the generalised form of Maxwell-Stefan equations, relationships have been developed and classified between the multicomponent and binary diffusion coefficients. By theorems of matrix calculus it was proved that strictly defined forms of the matrix of multicomponent diffusion coefficients fulfill the conditions specified above, i.e. they posses real and positive eigenvalues.