The effective conductivity &sgr;eof a dispersion of long, parallel cylinders (or two‐dimensional systems), distributed in a second continuous matrix phase, is determined as a function of its microscopic structure. We obtained an expression for the effective conductivity of two‐dimensional systems (based on an approximate scheme) that includes the one‐body and two‐body terms in the cluster expansion for &sgr;e. The effective conductivities of two‐dimensional hard disks and square‐well particles are computed. It is found that this expression yields excellent estimates for the effective conductivity over a wide range of cylinder volume fractions, and for cases in which the cylinder to matrix phase conductivity ratios are high.