A hierarchy of models is developed to test the accuracy of the family solution of the photochemical equations of the stratosphere. Results of the explicit solution of the equations for a simplified midwinter disturbance near the 850 K isentropic surface are compared with the solutions for models containing 26, 20, 16, 14, 12, 10, and 8 families for a 12-day integration. Ill general, it is found that the family approach can yield quite accurate solutions, providing enough families arc retained. However, large errors, of order 20%, arc produced in some radical concentrations such as OH for models with a small number of families. The minimum number of families consistent with economy in the solution of the equations while maintaining scientific accuracy is discussed. In particular, it is recommended that exact dynamical tracers be incorporated into family models to reduce computer memory requirements by parameterizing long time scale species such as H20, CH 4 and H 2 in terms of the tracer. Other species such as N20 , total chlorine, and total nitrogen may also be so parameterized according to how the model is to be used. Even for models with an extensive set of families, the concentrations of radical species are significantly in error at dawn, suggesting the nccd for caution in comparisons with measurements made using occultation techniques. This may not Icad to significant errors in the calculation of reservoir species such as O 3 on time scales up to a few weeks but can seriously perturb the qualitative features of other important molecules such as C1ONO 2 and CIO, and this could lead to significant errors in the calculation of O 3 in the longer tenn. The results have important implications for the development of three-dimensional models of stratosphcric chemistry. Some examples of the chemical schemes of those models which have boon described in the literature are studied to determine their strengths and weaknesses. The schemes arc shown to produce good results for species such as O• and HNO 3 but show signs of weaknesses, particularly in the radical species. Some changes to these schemes arc suggested, with a view toward producing an improved three-dimensional model in the future. l. Turco and Whitten [1974] discussed the accuracy of various computational techniques for solving aeronomic problems. This work showed that a family conservation approach could be quite accurate (at least for odd hydrogen species), providing the molecules do not undergo very large changes in concentration. Unfortunately, their work was restricted to analytical problems which did not include a representation of typical diurnal chemistry. Johnston and Podolske [1978], using a one-dimensional column model, showed negligible differences between the accurate solution of the equations and the solution assuming photochemical steady state. However, in their study, the solar zenith angle was fixed at 45 ø , and the results were divided by 2 to correspond to a diurnal average. Recently, Douglass et al. [1989] investigated the impact of changin...