  We report on the evidence for the multiband electronic transport in
$\alpha$-YbAlB$_{4}$ and $\alpha$-Yb$_{0.81(2)}$Sr$_{0.19(3)}$AlB$_{4}$.
Multiband transport reveals itself below 10 K in both compounds via Hall effect
measurements, whereas anisotropic magnetic ground state sets in below 3 K in
$\alpha$-Yb$_{0.81(2)}$Sr$_{0.19(3)}$AlB$_{4}$. Our results show that Sr$^{2+}$
substitution enhances conductivity, but does not change the quasiparticle mass
of bands induced by heavy fermion hybridization.
