In the present paper the authors establish conditions for the uniform stability and the uniform asymptotic stability of equilibria of systems with impulse effects described by systems of nonlinear, time-varying ordinary differential equations. Under mild additional assumptions, these sufficient conditions turn out to be necessary as well. For the case of time-invariant systems,vith impulse effects described by nonlinear ordinary differential equations, the above results are used to establish conditions under which the uniform asymptotic stability of equilibria can be deduced from the linearizations of such systems.