Let M be a von Neumann algebra. A maximal abelian *-subalgebra A in M is singular if the only unitaries in M that normalize A are those in A. This notion was first considered by Dixmier, who gave an example of a singular maximal abelian *-subalgebra in the separable hypertinite II, factor (see [5]). Later Pukanszky [lo] and Tauer [ 141 gave other examples, also in the hyperfinite II, factor. In [ 111 Pukanszky showed that some of his type III factors have singular maximal abelian *-subalgebras. In [ 151 Takesaki introduced a new type of maximal abelian *-subalgebras, that he called simple, and showed that they are singular. He gave examples of such algebras in the hyperlinite II, factor. In [ 161 Nielsen showed that every continuous IPTFI factor has simple (and thus singular) maximal abelian *subalgebras. Note that if M is a separable discrete factor, i.e., M= 9(S) for some separable Hilbert space R, and A c S(R) is maximal abelian, then A is the direct sum of an atomic algebra and a diffuse algebra. The atomic part is clearly not singular and by a theorem of von Neumann the diffuse part is also nonsingular (actually in both cases the normalizer generates all 9(Z)). Thus discrete factors do not have singular maximal abelian *-subalgebras. In this article we prove that all separable continuous semifinite von Neumann algebras and all separable factors of type III,, 0 Q 1~ 1, have singular maximal abelian *-subalgebras. In the semifmite case our result is in fact more general: if 5 c Aut(M) is a group of *-automorphisms of M, containing the inner automorphisms, S 2 Int(M), and with B/Int(M) countable, then there exists a maximal abelian *-subalgebra A in M such that the only automorphisms in g that normalize A are the inner automorphisms 151 0022-1236183 $3.00