Partial Lyapunov stability and partial Lipschitz stability in Flows are introduced. It is proved that a flow on a compact metric space is Lyapunov stable if and only if it is partial Lyapunov stable with respect to a c -dense subset of the real numbers. Also it is proved that a C r(r≥ 1) flow on a compact, connected Riemannian manifold is Lipschitz stable if and only if it is partial Lipschitz stable with respect to a c -dense subset of the real numbers. Moreover, the dynamical properties of transitive Lyapunov stable flows are studied.