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Nanoelectromechanical system oscillators have been proposed for a variety of applications, such as radio-frequency signal processing and ultrasensitive sensing. Carbon nanotube (CNT) oscillators demonstrated that the resonance frequency can be widely tuned and the motions can be self-detected. The resonant behaviours of two types of CNT oscillators with cantilevered and fixed-fixed CNT resonators are investigated by continuum mechanics-based multiphysics finite-element method simulations using a reduced order model. It is found that these two types of devices have different resonant responses when the DC bias changes: the resonant frequency of fixed-fixed CNTs increases as the DC bias increases, whereas the resonant frequency of cantilevered CNT devices decreases as the DC bias increases. The simulations also show that the fixed-fixed CNT oscillators have better tuning capabilities than the cantilevered CNT devices. Therefore in general fixed-fixed CNTs should be used in the oscillator designs, unless the unique resonant behaviour of the cantilevered devices is desired.