  We predict a spin anomalous-Hall unidirectional magnetoresistance (AH-UMR) in
conducting bilayers composed of a ferromagnetic layer and a nonmagnetic layer,
which does $\textit{not}$ rely on the spin Hall effect in the normal metal
layer$-$in stark contrast to the well-studied unidirectional spin-Hall
magnetoresistance$-$but, instead, arises from the spin anomalous Hall effect in
the ferromagnetic layer. Physically, it is the charge-spin conversion induced
by the spin anomalous Hall effect that conspires with the structural inversion
asymmetry to generate a net nonequilibrium spin density in the ferromagnetic
layer, which, in turn, modulates the resistance of the bilayer when the
direction of the applied current or the magnetization is reversed. The
dependences of the spin AH-UMR effect on materials and geometric parameters are
analyzed and compared with other nonlinear magnetoresistances. In particular,
we show that, in magnetic bilayers where spin anomalous Hall and spin Hall
effects are comparable, the overall UMR may undergo a sign change when the
thickness of either layer is varied, suggesting a scheme to quantify the spin
Hall or spin anomalous Hall angle via a nonlinear transport measurement.
