Experiments are described on tunneling into SnIn and PbBi alloys near their upper critical fields. In this regime, a theory by de Gennes predicts gapless superconductivity with a density of excited states whose energy scale is field-independent. This density of states is investigated in detail, both in the superconducting sheath regime near field parallel to the surface and in the vortex regime near field normal to the surface. We find excellent agreement between theory and experiment for the shape of the tunneling characteristic and reasonable agreement for its normalization. (Author).