We theoretically analyze the effective electronic and magnetic responses of a 3-dimensional nonlinear composite consisting of periodical arrays of wires and split-ring resonators(SRRs) embedded into a nonlinear dielectric.We calculate the dependences of the real parts and imaginary parts of the effective permittivity and permeability of the structure on the varying external magnetic field strength.We demonstrate that both the real parts of the effective permittivity and permeability have hysteresis structures.We also discuss the switching of the composite among right-handed materials,epsilon-negative materials,and mu-negative materials under different conditions,which can be controlled by a proper choice of the external magnetic field strength(intensity of incident electromagnetic waves) in a certain frequency range.