It has been shown recently that the effective conductivity Keff of anisotropic media depends on the shape of correlations <Indelman and Abramovich, 1994>. This property results from the analysis of the second-order expression of Keff in the log conductivity variance &sgr;2, which is derived in terms of quadratures and calculated by numerical integration for two- and three-dimensional flows and for exponential and Gaussian covariances. The present paper is a continuation of this study and aims at deriving an analytical closed-form expression of Keff at order &sgr;4 for the case of two-dimensional flow in lognormal anisotropic media of Gaussian log conductivity correlation. ¿ 1998 American Geophysical Union