ABSTRACT We present spectroscopic observations of the Be/X-ray binary X Per obtained during the period 2017 December–2020 January (MJD 58095–58865). In 2017 December, the H α, H β, and He i 6678 emission lines were symmetric with violet-to-red peak ratio V/R ≈ 1. During the first part of the period (2017 December–2018 August), the V/R ratio decreased to 0.5 and the asymmetry developed simultaneously in all three lines. In 2018 September, a third component with velocity ≈250 km s−1 appeared on the red side of the He i line profile. Later, this component emerged in H β, accompanied by the appearance of a red shoulder in H α. 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 vwave ≈ 1.1 ± 0.2 km s−1, and the eccentricity of the eccentric wave is ewave ≈ 0.29 ± 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.