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Parallel multisplitting nonlinear iterative methods are established forthe system of nonlinear algebraic equations Aψ(χ)+Tψ(χ)=b,with A,T∈L(Rn)being matrices ofparticular properties,(ψ),ψ:Rn→Rnbeing diagonal andcontinuous mappings, and b∈Rn a known vector; and theirglobal convergence are investigated in detail under weaker conditions.Some numerical computations show that the new methods have better convergence properties than the known ones in the literature.