Starting from the observation that the relations between Phocas and Maleïnoi were not good during the reign of Nicephorus II, given the fact that a) the Maleïnoi did not support Nicephorus Phocas in 963, b) the first revolt against him originated from his close relative Gregory Maleinos and that c) the accession to the throne of Nicephorus II did not mean the subsequent rise in the military hierarchy for the Maleïnoi, we will examine, in this study, the version according to which Eustathius Maleïnos could have been appointed as general of Antioch and Lykandos by John I Tzimiskes.