PÉGASE-HR is a code aimed at computing synthetic evolutive optical spectra of galaxies with a very high resolution (R=10 000, or dlambda=0.55) in the range Lambda=[4000, 6800] Angstroms. PÉGASE-HR is the result of combining the code PÉGASE.2 with the high-resolution stellar library ÉLODIE. This code can also be used at low resolution (R=200) over the range covered by the BaSeL library (from far UV to the near IR), and then produces the same results as PÉGASE.2. In PEGASE-HR, the BaSeL library is replaced by a grid of spectra interpolated from the high-resolution ÉLODIE library of stellar spectra. The ÉLODIE library is a stellar database of 1959 spectra for 1503 stars, observed with the echelle spectrograph ÉLODIE on the 193 cm telescope at the Observatoire de Haute Provence.