  We consider unital simple inductive limits of generalized dimension drop
C*-algebras They are so-called ASH-algebras and include all unital simple
AH-algebras and all dimension drop $C^*$-algebras. Suppose that $A$ is one of
these C*-algebras. We show that $A\otimes Q$ has tracial rank no more than one,
where $Q$ is the rational UHF-algebra. As a consequence, we obtain the
following classification result: Let $A$ and $B$ be two unital simple inductive
limits of generalized dimension drop algebras with no dimension growth. Then
$A\cong B$ if and only if they have the same Elliott invariant.
