We investigate the gross properties of the dense neutron star matter and the structure of the stars under the inÑuence of strong magnetic Ðelds, based on two nonlinear p [ u models of nuclear matter, i.e., the BB and the ZM models, within the relativistic mean-Ðeld approximation. Contrary to the results obtained in the linear p [ u model and the BB model, we Ðnd that the inÑuence of the magnetic Ðeld on the e †ective nucleon mass m* is not signiÐcant in the ZM model ; therefore, we predict that the neutrons in the interior of a neutron star might be superÑuid according to the ZM model, if there is a strong magnetic Ðeld in the interior of the star. Moreover, the equations of state (EOSs) will become softer and softer with the increase of the strength of the magnetic Ðeld B. We show the e †ects of the interior magnetic Ðelds on the gross properties of neutron stars, such as the critical masses, their corresponding radii, the moment of inertia, the crust masses, the crust moment of inertia, and the gravitational redshift in both nonlinear p [ u models.