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We classify all cohomogeneity one manifolds with principal orbitQ^111=SU(2)^3/U(1)^2 or M^110=(SU(3) x SU(2))/(SU(2) x U(1)) whose holonomy iscontained in Spin(7). Various metrics with different kinds of singular orbitscan be constructed by our methods. It turns out that the holonomy of ourmetrics is automatically SU(4) and that they are asymptotically conical.Moreover, we investigate the smoothness of the metrics at the singular orbit.

Special cohomogeneity one metrics with Q^111 or M^110 as principal orbit