A theory of static state feedback for multivariable continuous-time non-linear systems is formulated. The theory applies to systems described by differential equations of the formẋ(t) = ƒ(x(t)u(t)). The basic objective is to design static feedback compensators which achieve the following properties: (a) the state-space trajectory of the closed-loop system is confined within a specified subspace, and (b) the closed-loop system is internally stable. An explicit method for designing such compensators is developed. The construction of the compensators involves only quantities directly derived from the given functionƒ.