Use of a tunneling Hamiltonian model for thin proximity-effect sandwiches in high parallel fields has indicated the possibility of spin splitting the quasiparticle density of states past the point where the up- and down-spin densities of states will cross. This crossing is signified by a large zero-bias peak in the tunneling conductance. In this paper we review the theory leading to this prediction and present the results of spin-polarized tunneling experiments in Al-oxide-Mg-Al junctions. Measurements at 0.4 K on a sandwich with 40 of Al over 25 of Mg at fields from zero to 3.4 T (where the sandwich went into the normal state) were in qualitative agreement with the theoretical predictions, including the peak at zero bias at the higher field values. © 1980 The American Physical Society.