Ring means “not necessarily associative ring.” The general structure theory of nonassociative PI-rings (cf. [5, 8, 93) has been restricted by lack of a theorem permitting passage from fairly general classes of rings to central simple algebras of finite dimension. A natural attack on this problem would be to attempt to generalize Kaplansky’s theorem (every associative, primitive PI-algebra is central simple of finite dimension), but two difhculties immediately arise: (1) how do we suitably generalize “primitive” and (2) there exist nonassociative simple Jordan PI-algebras, with 1, of infinite dimension over their center. (Example: Any Jordan algebra of a symmetric bilinear form of an infinitedimensional vector space; since every element is aIgebraic of degree < 2, we have the identity S&X,, X,X,, X,X,2), where S, denotes the “standard polynomial.” We shall discuss this example more closely later, in Section 2.) In this note, we bypass these difficulties by considering prime rings (i.e., the product of any two nonzero ideals is nonzero) and by restricting the class of PI-rings to “normal” PI-rings. The main tool is the “central closure” of a prime ring, developed by Erickson, Martindale, and Osborn El]. The general results enable us to obtain a structure theory of normal Jordan PI-rings which closely parallels the theory of associative PI-rings and alternative PI-rings (cf. 191). Throughout this paper R is a ring having centroid Z(R).