A novel giant magnetoresistance memory effect has been observed in epitaxial Nd0.7Sr0.3MnOz thin films which have previously been found to exhibit a linear increase in conductivity on first application of magnetic field B. The resistivity of the films depends not only on the instantaneous applied held but also on the magnetic history of the sample. At T well below the temperature T-p, where the zero-field resistivity has a peak, the film enters a high-conductivity state (upon application of a magnetic field) which persists even when B is reduced to zero. The original ''zero'' field state is not recovered until the sample is warmed to T similar to T-p. Surprisingly, the dc magnetization exhibits only a weak irreversibility while the magnetoconductivity is markedly hysteretic. A possible explanation is proposed. (C) 1995 American Institute of Physics.