The present study develops a new size-dependent nonlinear model for the analysis of the behaviour of carbon nanotube-based resonators. In particular, based on modified couple stress theory, the fully nonlinear equations of motion of the carbon nanotube-based resonator are derived using Hamilton s principle, taking into account both the longitudinal and transverse displacements. Molecular dynamics simulation is then performed in order to verify the validity of the developed size-dependent continuum model at the nano scale. The nonlinear partial differential equations of motion of the system are discretized by means of the Galerkin technique, resulting in a high-dimensional reduced-order model of the system. The pseudo-arclength continuation technique is employed to examine the nonlinear resonant behaviour of the carbon nanotube-based resonator. A new universal pull-in formula is also developed for predicting the occurrence of the static pull-in and validated using numerical simulations.