Linear feedback stabilization of nonlinear systems is studied for systems whose linearization at an equilibrium point possesses a simple critical mode that is uncontrollable. The results complement previous work on the synthesis of nonlinear stabilizing control laws. The present work addresses continuous- time systems for which the linearization has either a simple zero eigenvalue or a pair of simple pure imaginary eigenvalues. Both the stability analysis and stabilizing control design employ results on stability of bifurcations of parametrized systems