The structure and superconductivity of several niobium and molybdenum-base superconducting alloys obtained by coevaporation were studied. The formation of an amorphous phase is shown to depend on both alloy composition and substrate temperature in a systematic way. The variation of the superconducting transition temperature with alloy composition is compared for amorphous and crystalline forms of the same alloy composition, and the factors which govern superconductivity are discussed. Results of superconductive tunneling experiments involving amorphous molybdenum-base alloys show a ratio of energy gap to transition temperature of about 3.5. These results are presented as evidence that these amorphous alloys are weak-coupling superconductors.