Phenomenological arguments are presented to clarify the singularity of static nonlinear response near the critical magnetic (or electric) field Hc. The singularity of nonlinear susceptibility χ(H) is connected with the expansion of the free energy Φ(m) as a function of a quantity (mc - m), where m is the normalized magnetization and mc its value at the critical field; i.e. if Φ(m) = a0 - a1(mc - m) + a2(mc - m)ψ…, then χ(H) ∼1/(Hc - H)γH; γH = (ψ- 2)/(ψ- 1). That is, for 1 ≪ ψ≪ 2, χ(H) is continuous, for ψ= 2, it is finite but discontinuous at H = Hc, and for ψ> 2, it is divergent. The index γH(or γE) is investigated in the one-dimensional exactly soluble magnetic systems at T = 0 and the two-dimensional ferroelectric (KDP) models at finite temperature. The value of γH is zero for a fermion system with repulsive delta-function interaction. γH is equal to 1/2 for the antiferromagnetic Heisenberg model. In the Hubbard model, γH is equal to 1/2 in the case of half-filled band, and γH is always zero other-wise. In the general two-dimensional ferroelectric models, there exists no critical electric field, though the Wu model has a critical field Ec with γE = 1/2.