Basic classes for four-manifolds not of simple type

We extend the notion of basic classes (for the Donaldson invariants) to 4-manifolds with $b^{+}>1$ which are (potentially) not of simple type or satisfy $b_1>0$. We also give a structure theorem for the Donaldson invariants of 4-manifolds with $b^{+}>1$, $b_1>0$ and of strong simple type.