A method is described to exploit asymptotic waveform evaluation (AWE) in the time-domain analysis of nonlinear circuits by using SPICE models for nonlinear devices such as diodes, transistors, etc. Although AWE has been used for linearized circuits only, the aim is to enhance the accuracy of the simulation while preserving the computational efficiency obtained with AWE and to eliminate the piecewise-linear modelling problem. Practical examples are given to illustrate significant improvements in accuracy. For circuits containing weakly nonlinear devices, it is demonstrated that this method is typically at least one order of magnitude faster than SPICE.