We have developed a two-dimensional pole-to-pole chemical model of the stratosphere extending from 8 to 38 km in altitude. Atmospheric motions are simulated by using mean vertical and meridional winds and eddy diffusion coefficients. In the results reported here we have computed seasonally averaged distributions of important odd nitrogen (NO, NO2, and HNO3) and odd hydrogen (H, OH, HO2, H2O2) compounds. Photodissociation of N2O leads to production of odd nitrogen in the stratosphere and the odd nitrogen is ultimately removed by downward transport into the troposphere and rain-out (modeled here by a rain-out lifetime of 30 days below 8-km altitude). Results are presented for a quasi-steady state in which seasonal cycles repeat themselves. Our results show significant latitudinal as well as vertical variations in the predicted species which emphasize the need for at least two dimensions in accurate stratospheric modeling. Computed concentrations are compared with observations when they exist. We stress the need for observations of the vertical profiles of N2O, HNO3, NO2, and NO at many more latitudes than are presently available in order to test our two-dimensional modeling approach adequately.