A new theory is proposed for estimating the effective behavior of nonl
inear composites. The theory involves the restatement of the effective
energy function of a nonlinear composite in terms of the energy funct
ion of an appropriately chosen linear composite with anisotropic phase
s. This allows the direct conversion of well-known estimates for linea
r composites into corresponding estimates for nonlinear ones. The resu
lting estimates are exact to second-order in the contrast and satisfy
all known bounds.