  We investigate the possibility of extending the Ashtekar theory to eight
dimensions. Our approach relies on two notions: the octonionic structure and
the MacDowell-Mansouri formalism generalized to a spacetime of signature 1+7.
The key mathematical tool for our construction is the self-dual (antiself-dual)
four-rank fully antisymmetric octonionic tensor. Our results may be of
particular interest in connection with a possible formulation of M-theory via
matroid theory.
