The evolution of the rotational and vibrational distributions of molecular hydrogen in a hydrogen plasma expansion is measured using laser induced fluorescence in the vacuum-UV range. The evolution of the distributions along the expansion axis shows the relaxation of the molecular hydrogen from the high temperature in the upstream region to the low ambient temperature in the downstream region. During the relaxation, the vibrational distribution, which has been recorded up to v=6, is almost frozen in the expansion and resembles a Boltzmann distribution at Tapproximate to2200 K. However, the rotational distributions, which have been recorded up to J=17 in v=2 and up to J=11 in v=3, cannot be described with a single Boltzmann distribution. In the course of the expansion, the lower rotational levels (J<5) adapt quickly to the ambient temperature (approximate to500 K), while the distribution of the higher rotational levels (J>7) is measured to be frozen in the expansion at a temperature between 2000 and 2500 K. A model based on rotation-translation energy transfer is used to describe the evolution of the rotational distribution of vibrational level v=2 in the plasma expansion. The behavior of the low rotational levels (J<5) is described satisfactory. However, the densities of the higher rotational levels decay faster than predicted. (C) 2004 American Institute of Physics.