A mathematical model was developed to describe a DC discharge of a Ne-Xe-HCl for excilamp. To achieve our aims we used a one-dimensional model of the cathode sheath coupled to a zero dimensional model of plasma with the external circuit. The spatial profiles of the electron density, ion density and the electric field were shown to exhibit distinct structures of glow discharge. A current in DC discharge increase in monotonous way until reaching 52 A at 225 ns. The breakdown delay times have been calculated, the plasma breakdown is occurring at 160.75ns. The orders of the values of the electric field (105 V/cm) are a condition of the good operation of the excimer lamp. This model permits us to have a good resolution of the sheath region, and to provide a quantitative analysis of the time evolution of the electrical and chemical discharge properties.