To demonstrate that adiabatic RF flippers impose an inherent geometric phase on the neutron polarization vector, we built a NSE setup consisting of two pairs of such flippers in a pulsed neutron beam. As is well known, the combined gradient and RF fields in each flipper - in the rotating frame - behave as a rotating field. The amplitude of this field in the first three flippers was kept maximum. For various amplitudes of the rotating field in the remaining flipper we measured the NSE pattern. Besides the shift of the NSE-point due to the variation of the dynamic phase, the NSE patterns show the development of the geometric phase.