In this paper, a framework for stability analyses of a typical inverter-based islanded microgrid with two types of nonlinear loads is presented, namely ideal constant power loads (CPLs), which are the loads supplied by tightly regulated power electronics converters, and dynamic CPLs, which are used to represent motor-drive systems with large time constants. The comprehensive dynamic model of the considered microgrid is first developed, based on which a bunch of small-signal models are deduced using Taylor expansion made at different stable operating points. Afterward, eigenvalue-theorem-based stability analysis and parametric sensitivity analysis are successively performed on the obtained small-signal models to verify the stability of the system, predict the system's unstable regions, and identify the effects of parameters on the stability boundaries. In the meantime, the impacts of different kinds of nonlinear loads on the system stability are studied. Hardware-in-the-loop (HIL) real-time simulation platform of a 30-kVA microgrid, which is mainly formed by a 10-kVA photovoltaic (PV) system, a 10-kVA wind energy conversion system, a 10-kVA lithium-ion battery energy storage system, and two CPLs, is established in Typhoon HIL 602 device. The validity of the theoretical results is verified by real-time simulation results.