Linear feedback stabilization of nonlinear systems is studied for syst
ems whose linearization at an equilibrium point possesses a simple cri
tical mode that is uncontrollable. The results complement previous wor
k 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 ei
genvalues. Both the stability analysis and stabilizing control design
employ results on stability of bifurcations of parameterized systems.