The effective medium theory is used to model a two-phase strongly nonlinear dielectric composite. More general effective nonlinear coefficients are determined which are not limited to the case of dilute inclusions. Our results obtained by using the decoupling technique and the variational method are compared and are in agreement with the experimental results by Gehr et al. [J. Opt. Soc. Am. B 14, 2310 (1997)].