The critical behavior of nonlinear properties in the component composites is studied. The first component is assumed to be nonlinear and obeys the nonlinear current (Ⅰ)-voltage (Ⅴ) characteristic of form formula I=g1V+χ1Vβ, while the second component is linear with I=g2V, where g1 and g2 are linear conductance of constituents and χ1 is the nonlinear susceptibility and β is nonlinear exponent. The volume fractions of two components are p and 1-p respectively. The critical exponents of effective response is calculated by means of effective medium approximation and the relative resistance fluctuation method, respectively. The conclusions are the critical exponents of linear conductance M(β)=1 and nonlinear susceptibility N(β)=(β+1)/2 for all spatial dimensions d can be obtained within the effective medium approximation; while based on the scaling theory of the relative resistance fluctuation, the critical exponents depends on arbitrary nonlinear β and spatial dimensions d.