Ferromagnetic materials used in the magnetoelectric (ME) magnetic field sensors have magnetic hysteresis which leads to hysteresis in magnetoelectric properties. This effect is useful biasing of magnetostriction phase in the ac magnetic sensors [1]. However, for dc magnetic field ME sensors [2] the hysteresis creates an uncertainty in the measured field value. In this paper we suggest to use limit cycle of magnetization to eliminate magnetic hysteresis in the ME dc field sensor. This method is also utilized for fluxgate magnetometers.  The sensor studied was a 25 mm x 5 mm layered structure consisting of mechanically coupled 0.5 mm thick lead zirconate-titanate (PZT) piezoelectric layer and 0.02 mm thick magnetostrictive Ni layer. In experiments ac pumping magnetic field h with frequency f = 120 Hz and dc magnetic field H were applied parallel to the long side of the structure. Amplitudes of the 1st and 3d voltage harmonics generated across the PZT layer was measured as a function of dc field H for different pumping fields h1=13 Oe and h2 = 200 Oe (See Fig.1. and Fig.2). It was shown that increase in h tends to decrease the hysteresis in the sensor signal. Hysteretic behavior of the 3d harmonic disappeared at h = 200 Oe, amplitude of the harmonic increased and u(3) vs H dependence became more linear in the low-H range as compared with the 1st harmonic.  The results allow to conclude that use of the limit cycle magnetization make it possible to create high-sensitivity hysteresis-free dc magnetic field ME sensors.  The work was supported by Ministry of Education and Science of Russia, project No 3.76.214K, and Russian Foundation for Basic Research.