The effectiveness of some iterative approaches to the computation of the electromagnetic scattering by nonlinear isotropic dielectric cylinders of arbitrary cross-sections is investigated in this paper. These approaches have been developed within the distorted-wave Born approximation, the classic first-order Born approximation, and the Rytov approximation. They are based on an integral equation formulation that defines an equivalent problem in which the interactions between harmonics are taken into account by coupling terms that can be made explicit, as the nonlinearity has been defined. In the case of Kerr-like nonlinearities and under the hypothesis of time-periodic transverse-magnetic incident fields, the effectiveness of these approaches is evaluated by means of several numerical simulations, concerning cylinders of different cross-sections. The results are compared with those obtained by applying an exact numerical methodology based on an optimization procedure.