In 1981, Stone conjectured that a fully semimonotone matrix is contained in In 1995, Murthy proved that for ifHere, we show that for matrices with some specific sign patterns this conjecture is true. Murthy showed that fully semimonotone Z-matrices are that is Here, we show that semimonotone Z-matrices are contained in that is, we exempt the condition of fully semimonotone with semimonotone. Further, we show the equivalency of -matrices and matrices for Z-matrices. Precisely, we are characterizing the matrices in These classes have been found to be interesting in view of the fact that these are processable by Lemke’s algorithm.