In this technical note, we consider the following problem: what passivity properties for a nonlinear system can be inferred when its linearization around an equilibrium point is known to be passive. We consider both continuous-time and discrete-time systems with feedthrough terms. Our main results show that when the linearized model is simultaneously strictly passive and strictly input passive, the nonlinear system is passive as well within a neighborhood of the equilibrium point around which the linearization is done.