For the physically accurate simulation of molecular gases, the CTC-DSMC method is developed by directly coupling classical trajectory calculations (CTC) for rigid and vibrating rotators with the direct simulation Monte Carlo (DSMC) method. Using the CTC-DSMC method for rigid rotators, the rotational relaxation of nitrogen through a normal shock wave is simulated by employing the accurate potential energy surface. The CTC-DSMC results agree well with the experimental results. The CTC-DSMC method for vibrating rotators is used for the simulation of the vibrational relaxation and dissociation of oxygen infinitely dilute in an isothermal heat bath of argon with the model potentials, where the test-particle procedure is efficiently employed. It is shown that the dissociation occurs preferentially from the upper rotational quantum levels over almost all the vibrational quantum levels and that the steady velocity, rotational, and vibrational distributions considerably deviate from the heat-bath equilibrium distributions. The CTC-DSMC calculation reasonably reproduces the experimental results measured in shock-heated dilute oxygen-argon mixtures. ©2001 American Institute of Physics.