We investigated the magnetoresistance of La2/3Ca1/3MnO3+δmagnetic thin films. Under certain conditions, the magnetoresistance curves show a remarkable hysteresis and the resistance becomes dependent on the magnetic history. A relaxation behavior of the resistance has also been observed. Hysteresis and relaxation of the resistance are very similar to the phenomena of magnetoviscosity of the magnetic moment in spin glasses and the magnetic aftereffect in hard magnets.