The purpose of this paper is to discuss several nonsymmetric difference equations. By this we mean that not all points are calculated by the same equation. Proofs of convergence will attempt to follow the methods of Richtmyer [4]. Nonsymmetric difference equations are well known at the present time. The Peaceman-Rachford alternating implicit scheme [3] has been quite successful. Recently, Saul'ev has introduced an alternating explicit method [2]. In establishing convergence of these methods the assumption seems to have been made that consistency of the individual equations assures consistency of the combined equations. The equation presented in ?1 of this paper will represent a counterexample to this assumption. The following notation is used: