In this article we show well-posedness for a relatively general semilinear parabolic system under nonhomogeneous Neumann boundary conditions and semi-linearities of (some) equilibrium reaction type. The result in here weakens previously made by Krautle and Mahato (Kra08, Kra11 and MB131, MB132, resp.) on the coefficients of the elliptic operator as well as on the boundary conditions considerably.