State-to-state cross sections and a survey of detailed balance for transitions among the vibrational and rotational (v, j) states of H 2 1 g + below 37 mE h as the result of collisions in the H 2 + H 2 system were determined by using the quasiclassical trajectory (QCT) method. Study of this system is necessary for an improved understanding of the kinetics in the interstellar medium to model processes occurring in the molecular clouds. sections were examined for agreement with microscopic reversibility. In the majority of cases the agreement was poor. Consequently the conclusion is that QCT is not a viable method for the evaluation of state-to-state rate coefficients in the H 2 + H 2 system.ii