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