We report the results of measurements of the low-temperature specific heat Cp(T) and the ac susceptibility χac(T) in low applied magnetic fields for a series of samples of Eu1-xCaxB 6. The anomalies in Cp(T), together with the results for χac(T) and M(H), confirm the onset of phase transitions to long range magnetic order for x < 0.7 and provide evidence that for x ≥ 0.7, the Eu moments, which are captured in large magnetic clusters with magnetic moments of the order of 260 μB, adopt a spin-glass type ground state. The data set allows to establish the low-temperature [ T,x] phase diagram of this alloy series. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2005.