The article deals with the Stokes resolvent system in an exterior domain in R^3 , under traction boundary conditions. Existence and uniqueness results are proved for solutions whose velocity part is W^{2,p} -regular, and whose pressure part admits an L^p -integrable gradient. It turned out there are two distinct classes of solutions of this kind. One of them consists of solutions whose velocity part has zero flux on the boundary of the exterior domain. The pressure part of the solutions in the other class is L^r -integrable near infinity. The article further deals with resolvent estimates allowing to define a "Stokes operator" which generates an analytic semigroup.