We study ground state phase diagrams for the MMX chains, using a one-dimensional dimerized 3/4-filled extended Hubbard-Peierls model with site diagonal and off-diagonal electron-lattice interactions. The ground states are obtained both in the Hartree-Fock approximation and by the exact diagonalization. We discuss magnetic properties of the MMX chains, (C) 2000 Elsevier Science B.V. All rights reserved.