  We prove that the M\"{o}bius function is linearly disjoint from an analytic
skew product on the $2$-torus. These flows are distal and can be irregular in
the sense that their ergodic averages need not exist for all points. The
previous cases for which such disjointness has been proved are all regular. We
also establish the linear disjointness of M\"{o}bius from various distal
homogeneous flows.
