Variations of the superhump period of V368 Peg: Monotonicity or frequency doubling? The superhumps have been detected during the superoutburst in 2000, justifying the SU UMa subtype classification. 6 nights of the CCD observations show the decrease of the photometric period with luminosity by a factor of 2.3 times. The observations were obtained by N.I.Ostrova, N.A.Katysheva and S.Yu.Shugarov from JD 2451789.41 to 2451799.56. The time series analysis was done using the programs by I.L.Andronov. The models of the smooth character of this dependence vs the "smooth variation + frequency doubling" may be suggested. However, any of these models may not be justified or ruled out because of lack of observations at the descending branch between the bright and faint states. Another possibility is the gradual decrease of the period with luminosity at maximum with a subsequent frequency doubling at some level, where the Fourier harmonic becomes dominant over the main wave. The period ratio does not justify the effect of precise superhump frequency doubling while changing from the superoutburst maximum to its end. New observations are needed to cover the "period - luminosity" relation more densely, with a high importance of multilongitude campaign, taking into account a rapid decline from the superoutburst. If the frequency doubling occurs, the brightness level should be detected, where it takes place. If not, the parameters of the smooth variation should be obtained for further theoretic explanation. The theoretical explanation of the photometric period change of V368 Peg is to be proposed. At the brightness maximum, the presence of the "shot noise" is registered. The details may be found in the paper accepted by "Notices of the Astronomical School" ("Vestnik Astronomicheskoj Shkoly", Ukraine). The Internet version in English is available at http://il-a.pochtamt.ru/V368_Peg.htm . N.I. Ostrova^1, I.L. Andronov^1, N.A.Katysheva^2 ^1 Department of Astronomy, Odessa National University, Odessa 65014 Ukraine, il-a@mail.ru, http://il-a.pochtamt.ru , http://il-a.hotbox.ru ^2 Sternberg State Astronomical Institute, Moscow State University, Moscow 119899 Russia, nk@sai.msu.ru, http://cataclysm.sai.msu.ru