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Abstract.If si is a W-* algebra of type II on separable Hilbert space H, then si is not normal.Let sé be a W-* algebra on separable Hilbert space H, and let 2£ be the center of sé. A W-* subalgebra 38 of sé is full in sé if &<=■ S §C\SS'.We define the relative commutant 88° of 3ä in sé to be SSC=3 §'C\sé, and say that ^ is normal in sé if 38=3$cc. Clearly if S8 is normal then 3S is full. We say that si is normal if 3$ is normal in sé for every full subalgebra J*of sé. As for results on normality for general W-* algebras, it is well known that any type I W-* algebra is normal [1, p. 307, Exercise 13]. In this paper we apply direct integral theory to show that if sé is of type II then sé is not normal. Corollary 2. 3Ü is normal in sé if and only if ¿% is full and âS(X) is normal in sé(X) ¡i-a.t.