We present a spectral analysis of the archival X-ray data of classical Nova V1974 Cygni 1992 (Nova Cygni 1992) obtained by the ROSAT Position Sensitive Proportional Counter (PSPC). The X-ray spectrum is fitted with a two-component model. The first component is a white dwarf atmosphere emission model developed for the remnants of classical novae near the Eddington luminosity. The model is used to fit the soft X-ray data in the similar to 0.1-1.0 keV range, where the bulk of emission is below 0.7 keV. The second component is a Raymond-Smith model of thermal plasma applied to the hard X-ray emission above similar to 1.0 keV. The postoutburst X-ray spectrum of the remnant white dwarf is examined in the context of evolution on the Hertzsprung-Russell diagram using an O-Ne- and a C-O-enhanced atmosphere emission model. A constant bolometric luminosity evolution is detected with increasing effective temperature and decreasing photospheric radius using the O-Ne-enhanced model. The unabsorbed soft X-ray flux for the constant bolometric luminosity phase is found to be in the range (1.7-2.2) x 10(-7) ergs s(-1) cm(-2). A peak effective temperature of 51 eV (5.9 x 10(5) K) is detected 511 days after outburst. We also present the spectral development of the hard X-ray component. It is found to evolve independently of the soft one. The maximum of the hard X-ray emission is reached at similar to 150 days after outburst with an unabsorbed flux of similar to 2.0 x 10(-11) ergs s(-1) cm(-2) corresponding to a luminosity of (0.8-2.0)x 10(34) ergs s(-1) at a 2-3 kpc source distance. The time evolution of the hard X-ray flux and the plasma temperatures decreasing from 10 keV to 1 keV suggest emission from shock-heated gas as the origin of the hard X-ray component.