PÉGASE (Projet d'Étude des GAlaxies par Synthèse Évolutive) is a code to compute the spectral evolution of galaxies. The evolution of the stars, gas and metals is followed for a law of star formation and a stellar initial mass function. The stellar evolutionary tracks extend from the main sequence to the white dwarf stage. The emission of the gas in HII regions is also taken into account. The main improvement in version 2 is the use of evolutionary tracks of different metallicities (from 10-4 to 5×solar). The effect of extinction by dust is also modelled using a radiative transfer code. PÉGASE.2 uses the BaSeL library of stellar spectra and can therefore synthesize low-resolution (R~200) ultraviolet to near-infrared spectra of Hubble sequence galaxies as well as of starbursts.