  We present spectroscopic observations of the Be/X-ray binary X Per obtained
during the period December 2017 - January 2020 (MJD~58095 - MJD~58865). In
December 2017 the $H\alpha$, $H\beta$, and HeI 6678 emission lines were
symmetric with violet-to-red peak ratio $V/R \approx 1$. During the first part
of the period (December 2017 - August 2018) the V/R-ratio decreased to 0.5 and
the asymmetry developed simultaneously in all three lines. In September 2018, a
third component with velocity $\approx 250$~km~s$^{-1}$ appeared on the red
side of the HeI line profile. Later this component emerged in $H\beta$,
accompanied by the appearance of a red shoulder in $H\alpha$. Assuming that it
is due to an eccentric wave in the circumstellar disc, we find that the
eccentric wave appeared first in the innermost part of the disc, it spreads out
with outflowing velocity $v_{wave} \approx 1.1 \pm 0.2 $~km~s$^{-1}$, and the
eccentricity of the eccentric wave is $e_{wave} \approx 0.29 \pm 0.07$. A
detailed understanding of the origin of such eccentricities would have
applications to a wide range of systems from planetary rings to AGNs.
