Consider a linear control system of the form: x = Ax + B(u). The approximately reachable set is the closure (in the state space X) of KAPPA_0 := {x(T): u be an element of SCRIPT U_ad}. We consider perturbation by a nonlinearity giving: x = Ax + F(x) + B(u) and ask when the corresponding {KAPPA COMPLEMENT}_F is the same as KAPPA COMPLEMENT_0 . The concern is to reduce this to analysis of the relation to KAPPA_0 of KAPPA_0, obtained from an affine perturbation: x = Ax + g + B(u), for g be an element of SCRIPT G.