This work extends previous research on numerical solution of nonlinear systems in musical acoustics to the realm of nonlinear musical circuits. Wave digital principles and nonlinear state-space simulators provide two alternative approaches explored in this work. These methods are used to simulate voltage amplification stages typically used in guitar distortion or amplifier circuits. Block level analysis of the entire circuit suggests a strategy based upon the nonlinear filter composition technique for connecting amplifier stages while accounting for the way these stages interact. Formulations are given for the bright switch, the diode clipper, a transistor amplifier, and a triode amplifier.