  In this letter we introduce a generalization of the Knizhnik- Zamolodchikov
equations from affine Lie algebras to a wide class of conformal field theories
(not necessarily rational). The new equations describe correlations functions
of primary fields and of a finite number of their descendents. Our proposal is
based on Nahm's concept of small spaces which provide adequate substitutes for
the lowest energy subspaces in modules of affine Lie algebras. We explain how
to construct the first order differential equations and investigate properties
of the associated connections, thereby preparing the grounds for an analysis of
quantum symmetries. The general considerations are illustrated in examples of
Virasoro minimal models.
