Suppose a rigid body moves steadily and without rotation in a viscous incompressible fluid, and the flow around the body is steady, too. Such a flow is usually described by the stationary Navier-Stokes system with Oseen term, in an exterior domain. An Oseen term arises because the velocity field is scaled in such a way that it vanishes at infinity. In the work at hand, such a velocity field, denoted by U, is considered as given. We study a solution of the incompressible evolutionary Navier-Stokes system with the same right-hand side and the same Dirichlet boundary conditions as the stationary problem, and with U+u_0 as initial data, where u_0 is a H^1-function. Under the assumption that the H^1-norm of u_0 is small (u_0 a ``perturbation of U'') and that the eigenvalues of a certain linear operator have negative real part, we show that the L^2-norm of the gradient of the difference v(t)-U tends to zero when t tends to infinity (''stability of v''), where v denotes the velocity part of the solution to the initial-boundary value problem under consideration.