We studied, both theoretically and experimentally, the ac magnetic response of type-II superconductors superimposed on a weak H_dc field. Theoretical simulations were made within the construct of the Kim-Anderson critical-state model, where the critical current density J_c is assumed to be given by J_c=k/(Bo+|Bi|). k and B_o are temperature-dependent material parameters, and B_i is the local flux density in the sample. We also measured complex susceptibilities Xn=X′n-iX″n (n=1, 2, 3, 5, 7) of a melt-processed YBa₂Cu₃O_y specimen and analyzed the observed Xn by applying the magnetization equations derived from the Kim-Anderson model. We found that the experimental results were qualitatively well reproduced. Present results indicate that, for a specimen of which J_c sensitively varies with B_i, the effect of a weak H_dc should be explicitly taken into consideration for studies of the ac magnetization.