Magnetic properties of A 2 BB O 6 (A = rare or alkaline-earth ions; B, B = transition-metal ions) double perovskites are of great interest due to their potential spintronic applications. Particularly fascinating is the zero-field-cooled exchange bias effect observed for the hole-doped La 2−x A x CoMnO 6 polycrystalline samples. In this paper we synthesize La 2 CoMnO 6 , La 1.5 Ca 0.5 CoMnO 6 , and La 1.5 Sr 0.5 CoMnO 6 single crystals by the floating zone method and study their magnetic behavior. The three materials are ferromagnetic. Surprisingly, we observe no zero or even conventional exchange bias effect for the Ca-and Sr-doped single crystals, in sharp contrast to polycrystalline samples. This absence indicates that the lack of grain boundaries and spin-glass-like behavior, not observed in our samples, might be key ingredients for the spontaneous exchange bias phenomena seen in polycrystalline samples.