Most models in economics and the applied sciences are solved by first order iterative techniques, usually based on the Gauss-Seidel algorithm. This paper examines the convergence of multiparameter extrapolations (accelerations) of first order iterations, as an improved approximation to the Newton method for solving arbitrary nonlinear equation systems. It generalises my earlier results on single parameter extrapolations. Richardson’s generalised method and deflation method for detecting successive solutions in nonlinear equations systms are also presented as multiparameter extrapolations of first order iterations. New convergence results are obtained for those methods.