This study addresses the development of probability distributions of travel times for one-dimensional (vertical) solute transport in soils. The field-scale soils are considered heterogeneous, with stationary fluctuations of soil hydraulic properties in the horizontal direction but nonstationary fluctuations of these properties in the vertical direction due to layering of the soil, which induces nonstationary heterogeneity. Approximate ensemble probability distribution functions of conservative solute travel time for vertical convective solute transport were derived directly from the convective transport stochastic partial differential equation, under both deterministic and stochastic soil surface water flux (infiltration rate) and under unsteady and nonuniform soil water flows. General depth-varying initial and time-varying boundary conditions were used in these derivations. The magnitude of the approximation in the theoretical probability distribution functions of travel time is quantified mathematically. Utilizing the soil water content data from a University of California, Davis, field site, it is shown that the mathematical condition for this approximation is satisfied for this field. The spatial heterogeneity is represented through a nonstationary soil water content random field which covaries both in time and in space. Dispersion emerges naturally in the derived ensemble probability distribution functions of solute travel time, owing to the stochasticity of soil water content at field scale. Then the theoretical expression for mean solute concentration over a field is derived, by means of the theoretical solute travel time distribution, as a function of time and soil depth, under vertical transport with rectangular pulse solute loading for the upper boundary condition. Comparisons of theoretical probability density functions of solute travel time against their empirical counterparts, obtained from field experimental observations under steady but nonuniform soil water flow, show good agreement. Comparisons of theoretical mean solute concentrations, as they evolve with time and soil depth, against field experimental observations also show good agreement. However, further field experiments under unsteady flow conditions are required for the comprehensive validation of the developed theory. ¿ American Geophysical Union 1996