The decoupling approximation developed by Stroud and Wood is employed
to study the effective response of a class of strongly nonlinear condu
cting composite media which obey a current-field relation of the form
J = chi\E\(2)E. The approximation allows us to convert established res
ults on linear composites to strongly nonlinear ones with identical mi
crostructures. The results are compared with published numerical simul
ation data and with the recently established bounds and estimates; goo
d agreement is found.