A tank for cryogenic liquids, which is intended for installation in motor vehicles and which consists of an outer container and of an inner container suspended in the latter in tension or compression struts. In order to take the contrasting requirements in motor vehicles into account in an optimum way, between the outer container and inner container abutments and supporting faces are additionally provided, which can be spaced apart from one another when the vehicle is at a standstill and can be brought to bear when the vehicle is driving. The abutments inside the outer container Co.-operate with supporting faces on the inner container and can be displaced by means of an actuator.