Stochastic analysis of steady state three-phase (water, oil, and air) flow in heterogeneous porous media was performed using the perturbation theory and spectral representation technique. The governing equations describing flow of water, oil, and air are coupled and nonlinear. The key stochastic input variables are intrinsic permeability, k, and the soil grain size distribution index, &agr;. Three different stochastic combinations of these two input parameters were considered in the analysis. The spectral/perturbation approach was used to develop closed-form expressions to describe stochastic variability of key output processes, such as capillary and individual phase pressures. The second paper of this two-part series <Abdin and Kaluarachchi, this issue> will discuss the applicability and the validity of the spectral/perturbation technique to study the stochastic behavior of three-phase flow using numerical simulations.¿ 1997 American Geophysical Union