In previous papers of this series we described an analytical-numerical method to predict deterministically solute transport under uncertainty based on a new Eulerian-Lagrangian theory. We examined the effect that conditioning on hydraulic data has on predicted velocities and concentrations due to instantaneous point and nonpoint sources and discussed the same effect on spatial plume moments, total mass flow rate across a ''compliance surface,'' cumulative mass release across this surface, and the corresponding travel time distribution. Our analysis to date assumed that the initial state of the plume (the source term or initial concentration) is known with certainty and that the groundwater velocity field is Gaussian. In reality, the initial state of the plume is almost never known with certainty, especially when this state is inferred by sampling a plume at some arbitrary time t0 following introduction of the solute into the subsurface (as is the case at many contaminated sites). Likewise, Monte Carlo simulations have shown that in Guassian log hydraulic conductivity or log transmissivity fields, of the kind often indicated by in situ hydraulic test data, the longitudinal velocity becomes rapidly lognormal as the variance of the heterogeneities increases. In this paper we show how to handle both of these complications by means of our analytical-numerical method of computation. By revisiting our previous examples, we explore the effects that uncertainty in plume initial state and non-Gaussian velocities may have on predicted plume concentrations and uncertainty due to instantaneous point and nonpoint sources with and without conditioning on measurements of log transmissivity or hydraulic head in two dimensions. One of our findings is that the more common Gaussian models are nonconservative (in a regulatory sense) when applied during early dimensionless times to plumes that are initially short in the direction of mean flow. ¿ American Geophysical Union 1995