A perturbation expansion method is used to study the effective thermal conductivity of nonlinear composite media with contact resistance. We overcome difficulties caused by the temperature discontinuity and temperature gradient singularity on surfaces between different phases where thermal contact resistance exists. A general definition of the effective thermal conductivity is proposed. Using the definition, we derive formulae for the effective linear and nonlinear thermal conductivities of composite media with low concentrations of cylindrical inclusions. Effects of thermal contact resistance on the effective thermal conductivities are discussed in detail.