An atmospheric pressure direct current (DC) plasma jet is investigated in N2 and dry air in terms of plasma properties and generation of active species in the active zone and the afterglow. The influence of working gases and the discharge current on plasma parameters and afterglow properties are studied. The electrical diagnostics show that discharge can be sustained in two different operating modes, depending on the current range: a self-pulsing regime at low current and a glow regime at high current. The gas temperature and the N2 vibrational temperature in the active zone of the jet and in the afterglow are determined by means of emission spectroscopy, based on fitting spectra of N2 second positive system (C3Π-B3Π) and the Boltzmann plot method, respectively. The spectra and temperature differences between the N2 and the air plasma jet are presented and analyzed. Space-resolved ozone and nitric oxide density measurements are carried out in the afterglow of the jet. The density of ozone, which is formed in the afterglow of nitrogen plasma jet, is quantitatively detected by an ozone monitor. The density of nitric oxide, which is generated only in the air plasma jet, is determined by means of mass-spectroscopy techniques.