EVOLUTION OF GALACTIC DISCS: TWO MODES OF STAR FORMATION ABSTRACT We develop the model of the evolution of surface gas density, stellar density, star formation rates and chemical composition of galactic disc taking into account the gravitational instability of rotating gaseous layer in the scales of several kpc. The central proposition was maden is the existence of two modes in the star formation. First mode associated with the large - scale grav.instability and takes place only when a local gas surface density is more than a critical value, which depends on the dynamical parameters of a gaseous disc. Second one don't associated with a large - scale grav.instability and determined by the surface density of the gas and stars. In the model we took into account the gas return from evolved stars, a radial movement of the gas in a spiral arms and accretion of the gas into the galactic disc. We found that our model is in a good agreement with observations for our Galaxy and for four others galaxies only if to assume relatively high low-mass limit for IMF ($1 \div 2 \, M_{\odot}$) at the mode I and upper-mass limit ($\approx 40\, M_{\odot}$) for mode II. The model distributions are in agreement with observations as for the cases with the accretion of the gas into the disc, as when no accretion.