Recent studies revealed specific features of chemical processes occurring on the surface of growing group-III nitrides – extremely low sticking probability of molecular nitrogen, low sticking coefficient and incomplete decomposition of ammonia frequently used as the nitrogen precursor. These features (kinetic by nature) result in the growth process going on under conditions remarkably deviated from the gas-solid heterogeneous equilibrium. In this paper we propose a novel approach to modeling of group-III nitride growth by MOVPE taking into account these features. In the model the sticking/evaporation coefficients of N2 and NH3 extracted from independent experiments are used allowing adequate description of the kinetic effects. The model is applied to analysis of growth of binary (GaN) and ternary (InGaN) compounds in a horizontal tube reactor. The growth rate and the solid phase composition are predicted theoretically and compared with available experimental data. The modeling results reveal lower ammonia decomposition ratio on the surface of the crystal as compared to thermodynamic expectations. The developed model can be used for optimization of growth process conditions.