The algebraic surfaces of revolution considered in this paper are generated either (a) by a circle or a lemniscate, or (b) by a Cartesian oval or especially a limacon of Pascal. The absolute circle at infinity is a double curve for the cyclides of type (a), in particular a cuspidal curve for the cyclides of type (b). Continuing earlier investigations on general cyclides there are deduced several remarkable properties of the spherical quartics situated on the mentioned cyclides of revolution.