  We have investigated line profiles in a large sample of Cepheid spectra, and
found four stars that show unusual (for Cepheids) line profile structure (bumps
or/and asymmetries). The profiles can be phase dependent but the behavior
persists over many cycles. The asymmetries are unlikely to be due to the
spectroscopic binarity of these stars or the specific velocity field in their
atmospheres caused by shock waves. As a preliminary hypothesis, we suggest that
the observed features on the line profiles in the spectra of X Sgr, V1334 Cyg,
EV Sct and BG Cru can be caused by the non-radial oscillations. It is possible
that these non-radial oscillations are connected to resonances between the
radial modes (3.2, 7.5 or 10.0 days).
