The crystal structures, homogeneity ranges and magnetic properties of the three Laves phases in the tantalum-cobalt alloy system have been studied with the aid of the X-ray powder photographs, density and magnetic measurements. The hexagonal MgNi_2-type TaCo_2 compound with the homogeneity range of about 25.5 to 27.0 at.% Ta, is ferromagnetic with Curie temperatures lower than 19 K and saturation magnetizations at 4.2 K less than 3.58 emu/g. The cubic MgCu_2-type one is paramagnetic down to 4.2 K over the whole homogeneity range of about 28.5 to 33.3 at.% Ta. If a relatively strong temperature-dependent magnetic susceptibility of the stoichiometric composition in this compound is analyzed as the band paramagnetism, excess cobalt atoms seem to have very small localized moments in the non-stoichiometric one. Around 40.0 at.% Ta one observed a hexagonal MgZn_2-type which shows Pauli-paramagnetism with the smallest magnetic susceptibility among the three Laves phases
