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Several methods have become available recently for the determination of the steady-state response of nonlinear circuits. The Newton algorithm is one of the more successful methods. However, in certain cases, the method fails to converge to a steady-state solution. Some modifications to the Newton method to increase convergence reliability or speed are proposed. The implementation of these modifications is discussed. Several example circuits are given and the results compared. Some guidelines for the use of these modified methods are also given.