This paper investigates the exponential stability of slowly time-varying nonlinear systems of the form \(\dot x= f(x,t\mid\alpha)\) and also of partially slowly time-varying systems \(\dot x= f(x,t,t\mid\alpha)\). A sufficient condition for exponential stability of a feedback interconnection of a slowly time-varying linear system and a time-varying sector nonlinearity is given. An example is included which demonstrates that the technique can be used to obtain an exponential stability result for a pendulum with a nonlinear partially slowly time-varying friction attaining positive and negative values.