  We introduce the concept of a Clifford-Weyl structure on a conformal
manifold, which consists of an even Clifford structure parallel with respect to
the tensor product of a metric connection on the Clifford bundle and a Weyl
structure on the manifold. We show that the Weyl structure is necessarily
closed except for some "generic" low-dimensional instances, where explicit
examples of non-closed Clifford-Weyl structures can be constructed.
