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An effective analytical model combining geometrical optics with the transfer-matrix theory for stratified optical media is applied to investigate the sensing properties of tapered optical fiber surface plasmon resonance (SPR) sensors incorporating Ag-Au bimetallic layers, particularly in the context of phase interrogation. The performance of the sensing structures is studied as a function of the tapering parameters and thickness of the metallic layers. It is shown that the Ag-Au bimetallic combination is capable of improving the resolution and tuning working region of SPR fiber-optic sensors and that by tapering the sensing structures enhanced sensitivity can be achieved when phase interrogation is considered.