The European XFEL GmbH is a new X-ray FEL facility expected to be lasing to users at the end of 2017. Three gap-movable SASE Undulator Systems are designed to produce FELs with tunable wavelengths from 0.05 to 5.2nm.*,** A total of 91 5m long undulator segments and phase shifters were magnetically tuned respecting tight specifications. Magnetic field hysteresis effects due to the gap shift of the Undulator System while changing the FEL radiation wavelength may impact the machine's operational mode. We report on these effects by either opening or closing the gap while performing field integrals measurements with moving wire technique. The undulator segments show negligible magnetic hysteresis and are expected to be operated with no influence to the FEL and beam trajectories in either feed forward or feed backward mode. The phase shifters show first field integrals hysteretic behavior of few G.cm which is comparable in magnitude to the allowed total field integrals and can be associated to the magnetization of the yoke structure. Phase shifters are magnetically tuned for that the feed forward mode (opening gap) fully satisfies the XFEL. EU magnetic specifications for beam operation. Proceedings of the 38th Int. Free Electron Laser Conf., FEL2017, Santa Fe, NM, USA