Possibilities of the optimum physical and mathematical description of determining functions for the equations of reological complex media are considered. Linear and nonlinear thermo-tenacity-elasticity, long durability functions and functions of the achievement of the limit of fluidity are analyzed. It is shown that for nontrivial heterogeneous media simple physical dependences are inapplicable. The kind of functions essentially depends on the concept on which the equation of state is based. The mathematical form of functions is of no lesser important than the physical form because the convenience of description, calculations and the chance of the conversion of this equation depends on it.