KZ equations are an essential tool in the study of conformal field theories with affine algebra symmetry. They are satisfied by all correlation functions of affine primary fields. However, string theory in AdS3 forces us to consider fields which are not affine primaries. I will explain that some generalizations of the KZ equations nevertheless still hold. I will discuss the implications of this finding for the relation with Liouville theory and the operator product expansion in the H3 model.