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We have formed superconducting contacts in which Cooper pairs incident from a thick In layer must move through a thin Nb layer to reach a semiconductor, either InAs or low temperature grown (LTG) GaAs. The effect of pair tunneling through the Nb layer can be seen by varying the temperature through the critical temperature of In. Several of the In/Nb-InAs devices display a peak in the differential conductance near zero-bias voltage, which is strong evidence of ballistic transport across the NS interface. The differential conductance of the In/Nb-(LTG) GaAs materials system displays conductance resonances of McMillan-Rowell type. These resonant levels exist within a band of conducting states inside the energy gap, formed from excess As incorporation into the (LTG) GaAs during growth. Electrons propagating in this band of states multiply reflect between the superconductor and a potential barrier in the GaAs conduction band to form the conductance resonances. A scattering state theory of the differential conductance, including Andreev reflections from the composite In/Nb contact, accounts for most qualitative features in the data.