We present tunneling data in the normal state of the electron doped cuprate superconductor Pr2-xCexCuO4 for three different values of the doping x. The normal state is obtained by applying a magnetic field greater than the upper critical field H-c2 for T< T-c. We observe an anomalous normal state gap near the Fermi level. From our analysis of the tunneling data we conclude that this is a feature of the normal state density of states. We discuss possible reasons for the formation of this gap and its implications for the nature of the charge carriers in the normal and the superconducting states of cuprate superconductors.
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