We have investigated the magnetoelectric (ME) effect in layered composite rings subjected to circumferential AC magnetic fields and DC magnetic fields in radial, axial or circumferential directions. Bilayer samples were obtained combining different grades of commercial Mn-Zn ferrites or Ni-Zn ferrites with commercial lead zirconate titanate (PZT). Mn-Zn ferrites with low magnetostriction saturation () and low magneto-crystalline anisotropy constants show high ME capabilities when associated with PZT in ring structures. In certain conditions, these ME effects are higher than those obtained with Terfenol-D/PZT composites in the same layered ring structure. Magnetostrictive and mechanical characterizations have given results that explain these high ME performances. Nevertheless, Mn-Zn ferrite/PZT composites exhibit voltages responses with low linearity especially at high signal level. Based on the particular structure of the ME device, a method to decrease the nonlinear harmonic distortion of the ME voltages is proposed. Harmonic distortion analysis of ME voltages measured in different configurations allows us to explain the phenomenon.