Problem of crystal growth process simulation for the cadmium-mercury-tellurium alloy from tellurium solution by the travelling heater method under microgravity conditions is considered. The main attention is drown to the formulation of boundary conditions at the interfaces and calculation of the growth rate. Limitation of the local thermodynamic equilibrium approximation and uncertainty in determination of growth parameters in this case is shown. Non-equilibrium model of HgCdTe crystal growth from solution is considered. It includes one matching parameter, the kinetic factor, which should be determined from experiment. Comparison of the calculation results obtained by the equilibrium and by the non-equilibrium rom experiment. Comparison of the calculation results obtained by the equilibrium and by the non-equilibrium model shows, that the kinetic factor does not influence the crystal growth rate since a certain value. Results of the calculation of HgCdTe crystal growth process at the seed from cadmium telluride are given as well.