We report here the studies of structural and magnetic properties of two equiatomic quaternary Heusler alloys CoCrVZ (Z = Al, Ga). Both the alloys crystallize in LiMgPdSn type crystal structure (space group #216) with B2 (CoCrVAl) and A2 (CoCrVGa) type anti-site disorder between elemental sites. Intended stoichiometry was confirmed from the compositional analysis. The temperature dependence of dc magnetic susceptibility and the low temperature moment values show a nearly compensating ferrimagnetic behaviour at low temperatures for both the alloys. The inverse of dc magnetic susceptibility starts to deviate from the Curie–Weiss law below 220 K and 164 K for the alloys containing Al and Ga respectively. The Arrott plots confirms the absence of long range order down to 2 K. Further analysis of the dc and ac susceptibility shows that the observed behaviour is due to the presence of Griffiths like phase in these alloys.