Binary mixtures of hydrazine and nitromethane were found to be non-ideal associated solutions. An equation of state (EOS) of the hydrazine-nitromethane solutions has been developed. This EOS takes into account the possibility of the formation of associated molecules due to interactions between hydrazine and nitromethane molecules. EOS parameters, including a possible chemical formula for the associate and its standard heat of formation and entropy, have been determined. Thermodynamic calculations of detonation parameters of the hydrazine-nitromethane system have been done by means of the TDS code for a wide range of hydrazine content in the explosive mixture (0-80 wt.%). The reliability of the results is guaranteed by using both an accurate, theoretically justified EOS for detonation products, which is derived from first principles of statistical mechanics, and realistic potentials for intermolecular interactions. It was shown that the use of the proposed EOS of the hydrazine-nitromethane solutions considerably improves the accuracy of the predicted detonation properties of the solutions and, furthermore, allows one to evaluate their shock sensitivity.