Consider the Oldroyd-B system on exterior domains with nonzero external forces f. It is shown that this system admits under smallness assumptions on f a bounded, global solution (u; τ), which is stable in the sense that any other global solution to this system starting in a sufficiently small neighborhood of (u(0); τ (0)) is tending to (u; τ). In addition, if the outer force is T-periodic and small enough, the Oldroyd-B system admits a T-periodic solution. Note that no smallness condition on the coupling coefficient is assumed.
