  To solve non-Hermitian linear system Ax=b on parallel and vector machines,
some paralell multisplitting methods are considered. In this work, in
particular: i) We establish the convergence results of the paralell
multisplitting methods, together with its relaxed version, some of which can be
regarded as generalizations of analogous results for the Hermitian positive
definite case; ii) We extend the positive-definite and skew-Hermitian splitting
(PSS) method methods in [{\em SIAM J. Sci. Comput.}, 26:844--863, 2005] to the
parallel PSS methods and propose the corresponding convergence results.
