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The classical nova V4743 Sgr was observed with XMM-Newton for about 10 hours on April 4 2003, 6.5 months after optical maximum. At this time, this nova had become the brightest supersoft X-ray source ever observed. We present the results of a time series analysis performed on the X-ray light curve obtained in this observation, and in a previous shorter observation done with Chandra 16 days earlier. Intense variability, with amplitude as large as 40% of the total flux, was observed both times. Similarities can be found between the two observations in the structure of the variations. Most of the variability is well represented as a combination of oscillations at a set of discrete frequencies lower than 1.7 mHz. At least five frequencies are constant over the 16 day time interval between the two observations. We suggest that a periods in the power spectrum of both light curves at the frequency of 0.75 mHz and its first harmonic are related to the spin period of the white dwarf in the system, and that other observed frequencies are signatures of nonradial white dwarf pulsations. A possible signal with a 24000 sec period is also found in the XMM-Newton light curve: a cycle and a half are clearly identified. This period is consistent with the 24278 s periodicity discovered in the optical light curve of the source and thought to be the orbital period of the nova binary system.