We present a method for solving systems of nonlinear equations suitabl
e for problems where convergence of an approximate Newton method is in
itially slow. The method, nonlinear elimination (NlEm), eliminates the
nonlinear equations and appropriate variables deemed to be causing th
e problem. An analysis of the method is given and leads to a detailed
algorithm that reduces automatically to an approximate Newton method n
ear the root of the system of nonlinear equations. Several examples ar
e given that demonstrate the efficacy of the method.