The intrinsic linear and nonlinear magnetic susceptibilities, χn, for a ferromagnet of arbitrary spin, calculated using the mean-field approximation, are shown to diverge in the asymptotic critical region (ACR) with the exponent γn = nγ + (n − 1)β and n = 1, 2, . . . . This behaviour of χn in the ACR is consistent with the scaling equation of state. With increasing spin, the divergence in χn(T ), as the ferromagnetic-paramagnetic phase transition temperature, TC , is approached from below or above, progressively slows down with the result that the width of the ACR increases. For a given spin, the higher the order of nonlinear susceptibility, the narrower the ACR. These results are in qualitative agreement with the critical behaviour of χn(T ) observed in an archetypal ferromagnet.