A device for determining the abnormal degree of deterioration of catalyst of a catalytic converter arranged in an internal combustion engine exhaust system is disclosed. The device comprises ability value grasping means for grasping an ability value in relation with a current purification ability of the catalyst and varying amount grasping means for grasping a varying amount of the ability value grasped by the ability value grasping means. It is determined that the degree of deterioration of the catalyst is abnormal when the varying amount grasped by the varying amount grasping means is smaller than a predetermined value.