The nonlinear response of an erbium-doped fiber amplifier is investigated theoretically through the use of nonlinear Fourier transfer functions, which are derived with the help of Volterra series. The influence of signal power, pump power, and frequency on the amplifier's nonlinear response is investigated. Results computed from the nonlinear transfer functions compare well with the numerical solution of the power evolution and rate equations. Moreover, the nonlinearity-induced distortion product is discussed. The performance evaluation of cascading systems by employing closed-form expressions for nonlinear transfer functions is discussed also.