  We report on progress in calculation of the spin-orbit interaction for the
HD$^+$ molecular ion. This interaction is currently the largest source of
theoretical uncertainty in determination of the hyperfine structure of
rovibrational transition lines. The corrections of order $m\alpha^7\ln(\alpha)$
are derived and numerically calculated. Theoretical hyperfine intervals are
compared with experimental data, and the observed discrepancies are discussed.
