This paper is an investigation of the correlation model for transport of nonreactive solutes in media with random porosity and permeability. The method of perturbation is used to obtain a second-order approximate, nonlocal (integrodifferential) equation for mean concentration. An approximate method of localization is used to convert to with the same order of approximation differential equations of transport. Exact averaged equations for one-dimensional transport are examined, and the question of the consistency and asymptotic behavior for approximate averaged equations is discussed. A detailed investigation of transport in a stratified system has been carried out. The second moment of concentration is examined, the variance of the concentration is computed, and cross-correlation moments are obtained for fields of porosity and velocity, including solute concentration. ¿ American Geophysical Union 1993