Reluctance synchronous machines, particularly the newer ones with axially laminated anisotropic rotor, are being employed increasingly in many industrial applications as they offer energy efficient solutions along with low-cost rugged construction and zero speed regulation. High-performance requirements of the machine demand a high saliency ratio resulting in low air-gap length along the direct axis. Air-gap eccentricity diagnosis therefore becomes very significant. In this paper, the effects of different types of eccentricity faults in a commercially available reluctance synchronous motor (RSM) are first analyzed to identify the fault-specific frequency components in the line current spectrum. For validating the analyses, a modified-winding-function-based model and a finite-element-based model are built to simulate the motor under different eccentricity conditions. Experiments are then carried out on a three-phase RSM with a moderate to high level of eccentricity to confirm the theoretical prediction and simulation results. Finally, by applying residue-elimination technique, the effects of supply unbalance and internal asymmetry are minimized, and eccentricity is detected very reliably. These results will help noninvasive eccentricity fault detection in larger power salient-pole synchronous machines in the long run.