  For a pair (algebra, module) with equidimensional and isolated singularity we
establish the existence of a versal henselian deformation. Obstruction theory
in terms of an Andr\'e-Quillen cohomology for pairs is a central ingredient in
the Artin theory used. In particular we give a long exact sequence relating the
algebra cohomology and the module cohomology with the cohomology of the pair
and define a Kodaira-Spencer class for pairs. Cohen-Macaulay approximation
induces maps between versal base spaces for pairs and cohomology conditions
imply properties like smoothness, isomorphism and linear section.
