In this paper the decoupling problem of the general muitivariable analytic nonlinear system of the form ẋ = ƒ(x, u),y = h(x,u) is discussed, where the state space is a real analytic manifold. Sufficient and necessary conditions for decoupling by state feedback combined with compensation and state feedback only are represented, A sufficient and necessary condition for stable decoupling is also derived. For decouplable systems the synthesis procedure is represented.