Two XMM-Newton observations of the fast classical nova V2491 Cyg were carried out in short succession on days 39.93 and 49.62 after discovery, during the supersoft source (SSS) phase, yielding simultaneous X-ray and UV light curves and high-resolution X-ray spectra. The first X-ray light curve is highly variable, showing oscillations with a period of 37.2 minutes after an extended factor of three decline lasting ~3 hr, while the second X-ray light curve is less variable. The cause of the dip is currently unexplained and has most likely the same origin as similar events in the early SSS light curves of the novae V4743 Sgr and RS Oph, as it occurred on the same timescale. The oscillations are not present during the dip minimum and also not in the second observation. The UV light curves are variable but contain no dips and no period. High-resolution X-ray spectra are presented for four intervals of differing intensity. All spectra are atmospheric continua with deep absorption lines and absorption edges. Two interstellar lines of O I and N I are clearly seen at their rest wavelengths, while a large number of high-ionization absorption lines are found at blueshifts indicating an expansion velocity of 3000-3400 km s-1, which does not change significantly during the epochs of observation. Comparisons with the slower nova V4743 Sgr and the symbiotic recurrent nova RS Oph are presented. The SSS spectrum of V4743 Sgr is much softer with broader and more complex photospheric absorption lines. The ejecta are extended, allowing us to view a larger range of the radial velocity profile. Meanwhile, the absorption lines in RS Oph are as narrow as in V2491 Cyg, but they are less blueshifted. A remarkable similarity in the continua of V2491 Cyg and RS Oph is found. The only differences are smaller line shifts and additional emission lines in RS Oph that are related to the presence of a dense stellar wind from the evolved companion. Three unidentified absorption lines are present in the X-ray spectra of all three novae, with projected rest wavelengths 26.05 Å, 29.45 Å, and 30.0 Å. No entirely satisfactory spectral model is currently available for the soft X-ray spectra of novae in outburst, and careful discussion of assumptions is required.
