We report on x-ray diffraction, magnetic susceptibility, electron-spin resonance, and heat-capacity studies of Co [Al1-x Cox] 2 O4 for Co concentrations 0≤x≤1. In this spinel system only the A -site Co2+ cation is magnetic, while the nonmagnetic B -site Al3+ is substituted by the low-spin nonmagnetic Co3+, and it is possible to investigate the complete phase diagram from Co2+ Al 3+ 2 O4 to Co2+ Co 3+ 2 O4. All samples reveal large negative Curie-Weiss temperatures ΘCW of the order of -110 K independent of concentration, which is attributed to a high multiplicity of the superexchange interactions between the A -site Co2+ cations. A pure antiferromagnetic state is found for x=1.0 and 0.9 with Néel temperatures TN =29.5 and 21.2 K, respectively, as evidenced by lambdalike anomalies in the specific heat. Compositions with 0.3≤x≤0.75 show smeared out strongly reduced magnetic ordering temperatures. At low temperatures, a T2.5 dependence of the specific heat is indicative of a spin-liquid state. For x≤0.2 a T2 dependence of the specific heat and a spin-glass-like behavior of the susceptibility below Tf ∼4.7 K are observed. The high value of the frustration parameter f= ΘCW/Tf >10 indicates the presence of strong spin frustration at least for x≤0.6. The frustration mechanism is attributed to competing nearest-neighbor and next-nearest-neighbor superexchange interactions between the A -site Co2+ ions.