By the use of nonequilibrium molecular dynamics we have studied the stress relaxation following imposition of a constant-volume elongation in the x(1) direction on a model diatomic liquid. Three consecutive modes of relaxation of the stress difference tau=t(11)-1/2(t(22)+t(33)) are found, each governed by exponentials e(-alpha it) with alpha(1) > alpha(2) > alpha(3). Each mode is shown to correspond to the return to isotropy of a different characteristic of the liquid structure that has been rendered anisotropic by the deformation, namely (1) (r) over bar (theta), the mean distance from a generic atom of interacting atoms in the theta direction, with the angle theta measured from the stretch axis x(1); (2) (N) over bar(theta), the mean number density of interacting atoms in the theta direction; and (3) [[P-2(theta(b))]], a measure of the orientation theta(b) of molecular axes with respect to x(1). The first two modes are identical in form to those studied previously [R. C. Picu and J. H. Weiner, J. Chem. Phys. 107, 7214 (1997)] for stress relaxation in a monatomic liquid, but their rates of decay differ because of differences in packing and in atomic mobility. During the third mode of relaxation it is found that tau=C[[P-2(theta(b))]], where C may be understood in terms of the intrinsic stress tensor, a tensor referred to a coordinate system fixed to the molecule [J. Gao and J. Il. Weiner, J. Chem. Phys. 90, 6749 (1989)]. The relevance of these results to stress relaxation in polymer melts is discussed.