We investigate the structural changes that accompany the stress relaxation in simple liquids by means of nonequilibrium molecular dynamics (NEMD) simulations. It is shown that during elongational deformation of the system, the statistical distribution of interacting neighbors about a given atom in the system, as measured by the mean interatomic distance in an arbitrary direction, becomes ellipsoidal with the largest semiaxis oriented in the stretch direction. Also, the mean number of particles in the distribution is smaller in that direction than normal to the stretch axis. Therefore, the return to isotropy consists on the one hand of a return of the spatial distribution of neighbors to the spherical shape and, on the other hand, of an isotropization of the number density distribution. These two processes, which take place with widely different rates, errs shown to be closely related to the two modes of stress relaxation characteristic for the simple liquids. The first of these, which is the fastest and corresponds to the most significant stress decay, is shown to be related to the fast return of the distribution of neighbors to the spherical shape. The second mode is intimately related to the isotropization of the density distribution on the sphere through a quasidiffusional process. (C) 1997 American Institute of Physics.