Vaidyanathan (1999) and Ferreira (1999) reported on nonlinear systems with exponential eigenfunctions. In this letter, we introduce a larger class of such systems, generated from a special family of exponential-input/constant-output operators that capture exponential signals from general inputs. In particular, we extend the classes of systems with exponential eigenfunctions defined in Vaidyanathan and Ferreira to include causal nonhomogeneous time-varying systems.