The relaxation of the energy stored in the translational and rotational degrees of freedom of N-2 and CH4 in the course of free jet expansions has been experimentally studied. Rotational temperatures along;he expansion axis were obtained by means of stimulated Raman spectroscopy, and terminal flow velocities and translational temperatures were determined item supersonic beam time-of-flight measurements. From these measurements low-temperature cross sections for rotational relaxation have been estimated. The results are compared with data from other experiments, and the validity of simple relaxation models is discussed.