Spin-orbit (SO) splitting, \(\pm \omega_{SO}\), of the electron Fermi surface in two-dimensional systems manifests itself in the interaction-induced corrections to the tunneling density of states, \(\nu (\epsilon)\). Namely, in the case of a smooth disorder, it gives rise to the satellites of a zero-bias anomaly at energies \(\epsilon=\pm 2\omega_{SO}\). Zeeman splitting, \(\pm \omega_{Z}\), in a weak parallel magnetic field causes a narrow {\em plateau} of a width \(\delta\epsilon=2\omega_{Z}\) at the top of each sharp satellite peak. As \(\omega_{Z}\) exceeds \(\omega_{SO}\), the SO satellites cross over to the conventional narrow maxima at \(\epsilon = \pm 2\omega_{Z}\) with SO-induced plateaus \(\delta\epsilon=2\omega_{SO}\) at the tops.