Traditional　procedures　to　treat　vibrations　of　gyroscopic　continua　involve　direct　application　of　perturbation　methods　to　a　system　with　both　a　strong　gyroscopic　term　and　other　weakly　coupled　terms.　In　this　study,　a　gyroscopic　modes　decoupling　method　is　used　to　obtain　an　equivalent　system　with　decoupled　gyroscopic　modes　having　only　weak　couplings.　Taking　the　axially　moving　string　as　an　example,　the　instability　boundaries　in　the　vicinity　of　parametric　resonances　are　detected　using　both　the　traditional　coupled　gyroscopic　system　and　our　system　with　decoupled　gyroscopic　modes,　and　the　results　are　compared　to　show　the　advantages　and　disadvantages　of　each　method.