Among theternary molybdenum sulfide compounds MMo6S8, we studied those with M=Eu, Ba, Sr and Ca by means of specific heat, electrical resistivity and low-temperature X-ray diffractometry. We observed in each case a structural phase transformation occurring below room temperature. The resulting low-temperature phase modification is characterized by an electronic density of states at the Fermi level which is too small to permit superconductivity. We anticipate that these compounds should exhibit superconductivity under pressure.