Time-dependent characteristics of the dielectric barrier discharge in Xe-Cl2 mixture at chlorine concentration of 0.5% and kinetic processes governing the generation of XeCl∗ molecules are studied using the 1D fluid model. It is shown that at low voltage amplitude (5 kV) a one-peak mode of the discharge is observed and at high voltage amplitude (7 kV) a two-peak mode of the discharge appears. The radiation power of the XeCl∗ band increases with amplitude of the supply voltage. It is demonstrated that the harpoon reaction Xe∗ + Cl2 → XeCl∗ + Cl provides the greatest contribution into generation of XeCl∗ exciplex molecules during short current pulses and the ion-ion recombination Xe+ 2 + Cl- → XeCl∗ + Xe provides the greatest contribution during afterglow. Quenching of XeCl∗ molecules is a result of the radiative decay XeCl∗ → Xe + Cl + hv (308 nm). During current spike the great contribution into quenching of XeCl∗ provides also the dissociative ionization e + XeCl∗ → Xe+ + Cl + 2e.