  We present a construction of superconformal field theories for manifolds with
Spin(7) holonomy. Geometrically these models correspond to the realization of
Spin(7) manifolds as anti-holomorphic quotients of Calabi-Yau fourfolds.
Describing the fourfolds as Gepner models and requiring anomaly cancellation we
determine the resulting Betti numbers of the Spin(7) superconformal field
theory. As in the G_2 case, we find that the Gepner model and the geometric
result disagree.
