Sufficient conditions for the system ẋ=f(x) = u(t)g{x} x ?R2n, to be stabilized via a smooth state feedback are given. It is also shown that certain Lie algebraic conditions are necessary and sufficient for the system to be feedback-equivalent to a system of controlled linear coupled oscillators, which is feedback stabilizable and which is proposed as a reference model for stabilization problems. Two overlapping sets of sufficient conditions which guarantee the existence and the explicit construction of stabilizing smooth state feedback controls are therefore given and their connections are discussed.