The ESR spectra of CoO-Al2O3, MoO3-Al2O3 and CoO-MoO3-Al2O3 were investigated in the oxidized state and after redn. with H2 + H2S (sometimes followed by a further treatment with H2) or by H2. All Co-contg. samples produce signals at 1200 Oe (for g-Al2O3) which shift to 1750 and 4300 Oe after treatment at 1300 Deg (formation of a-Al2O3). The signals are assigned to Co2+ in tetrahedral sites in the support; they are not affected by sulfiding or redn. If no Mo is present, redn. leads to the formation of an extremely broad and strong signal ascribed to Co metal; it is eliminated by the presence of Mo. In the absence of Co and in the oxidized state Mo-contg. samples develop a weak signal at g = 1.93, assigned to traces of Mo5+ in free MoO3; in the presence of Co this signal disappears. Pretreatment of Mo-contg. samples with H2 + H2S leads first to a hundredfold enhancement of the signal which, however, disappears after application of longer redn. times or higher temps. No signal connected with Mo3+ could be found. Finally, H2 after H2 + H2S treatments produced a signal at g = 2.16 if Co was present; it is assigned to either Co+ or Co2+ (low spin). A catalyst model is proposed containing 2 solid states. State I is the support with Co2+ and Mo6+ in its subsurface layers. Its fate after redn. is uncertain but Co2+ is not changed. State II is a separate system of compds. Co3O4, MoO3, or CoMoO4, depending on the compn. Treatments with H2 + H2S lead, resp., to Co + CoS, MoS2, or CoS + MoS2 (CoMo2S4).