This chapter deals with the simulation or analysis of a nonlinear electrical circuit by means of a computer program. It describes some algorithms for solving a set of nonlinear algebraic equations and nonlinear differential equations. The program creates and solves the differential-algebraic equations of a model of the circuit. The basic tools in the solution process are linearization, difference approximation, and the solution of a set of linear equations. A model is satisfactory if there is good agreement between measurements and simulation results. In this case, simulation may be used instead of measurement for obtaining a better understanding of the nature and abilities of the circuit. Since 1960, a large number of circuit-simulation programs have been developed by universities, industrial companies, and commercial software companies. In particular, the Simulation Program with Integrated Circuit Emphasis program has become a standard simulator both in the industry and in academia.