In this paper, we establish a class of asynchronous parallel nonlinear multisplitting relaxation methods for solving system of nonlinear equations. With special choices of the relaxed parameters in the new methods, not only can the convergence properties of them be improved, but also many applicable and efficient asynchronous parallel nonlinear multisplitting iteration methods such as the Jacobi, Gauss-Seidel, SOR as well as the asynchronous parallel nonlinear multisplitting AOR-Newton, -Chord and -Steffensen programs, etc., can be obtained. Under proper conditions, we build convergence theories about these asynchronous methods, and estimate their asymptotic convergence rates in detailed manner.