Recently the authors presented an accurate (in the variance of fluctuating log conductivity), second-order solution to the steady, saturated flow problem. The longitudinal, second spatial moment was evaluated numerically on the basis of the perturbation solution, and it was found that second-order corrections to the head field had little effect on this moment. Here we use the same theory and evaluate the second, transverse spatial moment. We find, in agreement with others, that our theory suggests that the second-order head corrections, as well as the nonlinear velocity corrections, are important. ¿ 1998 American Geophysical Union