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 ro-vibrational 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.[graphic not available: see fulltext][graphic not available: see fulltext]