A method is presented for solving the stiff differential equations for photochemical production and loss in the troposphere. The method is based on analysis of sources and sinks of odd-hydrogen radicals. The implicit equations are reduced to a single equation for OH which is solved in terms of odd-H production and loss. Individual odd-H sources and sinks are shown to have a simple functional dependence on OH. The resulting iterative process decreases computation time by a factor of 7 with little loss of accuracy and is applicable to both urban and remote tropospheric conditions. A discussion the odd-H budget and photochemical behavior in the troposphere is included. ¿ American Geophysical Union 1991