Accurate and dynamic behavioral models of SSPAS become of prime importance in system level analysis and design of modern communication and detection systems. This paper describes a new method to characterize and reproduce nonlinear memory effects in behavioral models of SSPAS. We highlight, in a first section, the detailed mathematical development, whose the starting point is the Volterra series expansion, and ends to the nonlinear impulse response notion. The new model extraction relies on envelope transient simulations or timedomain measurements of complex envelopes at extern OUT reference accesses. This modeling technique is simple and enables a good prediction of nonlinear memory effects and especially long term memory effects and nonlinear transient behaviors. Simulations and measurements based extractions of this model are presented through significant amplifier examples.