Nano-electro-mechanical system (NEMS) resonators have been widely used in multiple applications. However, their nonlinear behaviour has been considered as a nuisance until recent breakthroughs have illuminated the potential applications of nonlinear NEMS resonators such as neuromorphic computing and dynamic range enhancement for sensing applications. A comprehensive characterisation of the nonlinear behaviour is crucial for effective control, particularly in these emerging applications. This thesis reports a novel method to characterise nonlinear dynamics in doubly-clamped NEMS resonators by employing a novel parameter β_m extracted via perturbation series to quantify mechanical nonlinearity. Electrostatic nonlinearity is derived into explicit expression to incorporate with β_m to define the overall nonlinearity of the system. This method successfully explains the observed dependencies of nonlinear characteristics on DC actuation voltage and driving power under frequency modulation and 1-ω mixing measurement schemes. Result shows the value of β_m for NEMS with length of 2, 1.5, 1 μm is -1.5 ×10^(-5), -5.4×10^(-5), -2.8 × 10-5 m-2, respectively, regardless of measurement schemes, indicating the β_m is an intrinsic property that only relates to the NEMS material and design. Moreover, this research presents a novel method for identifying the onset of hysteresis with β_m. Through the analysis of NEMS beams of dimensions 2 μm and 1 μm, the hysteresis is expected to occur when DC at 1.61 V and 3.58 V, respectively. This result is later verified by experimental evidence. Furthermore, this study achieves the analysis systematic nonlinear response up to frequencies of 221 MHz, offering insights applicable to scaled NEMS resonators and emerging applications reliant on essential nonlinearity for device and system operations.