Aircraft operators rely on gas path analysis techniques for monitoring the performance and health of their gas turbine engine assets. This is accomplished by analyzing discernable shifts in measurement parameters acquired from the engine. This paper reviews the founding mathematical principles of gas path analysis, including conventional approaches applied for estimating engine performance deterioration. Considerations for extending the application of gas path analysis techniques to electrified aircraft propulsion (EAP) systems are also discussed, and simulated results from their application to an EAP concept comprised of turbomachinery and electrical system hardware are provided. Results are provided comparing the parameter estimation accuracy offered by taking a whole-system approach toward the problem setup versus that offered by analyzing each subsystem individually. For the latter, the importance of having accurate direct or inferred measurements of external mechanical torque loads placed upon turbomachinery shafts is emphasized.