A family of protozoan parasites (class Sporozoea, order Piroplasmida) occurring in the red blood cells of various mammals. The organisms, which are piriform, round, or oval, reproduce by schizogony to form tetrads or by binary fission to form pairs in the red blood cells; transmission is effected by ticks. The family includes the genera Babesia, Echinozoon, and Entopolypoides; Aegyptianella, formerly included, is now thought to be a rickettsia.Theileriidae.