  A classification is given of certain separable nuclear C*-algebras not
necessarily of real rank zero, namely the class of simple C*-algebras which are
inductive limits of continuous-trace C*-algebras whose building blocks have
their spectrum homeomorphic to the interval [0,1] or to a finite disjoint union
of closed intervals. In particular, a classification of those stably AI
algebras which are inductive limits of hereditary sub-C*-algebras of interval
algebras is obtained. Also, the range of the invariant is calculated.
