In this study, the nonlinear vibration response and instability behavior of double-walled carbon nanotubes (DWCNTs) subjected to electrostatic actuation are investigated. Both deterministic and stochastic modeling are considered. In deterministic modeling, two Euler–Bernoulli beams are adopted to model the inner and outer layers of the DWCNTs. The governing equations of motion are solved by Galerkin and multiple scales methods for primary and secondary resonances. The frequency response of the system is obtained as a function of some of the system parameters. The stability analysis of the response is performed and bifurcation points are obtained. In stochastic modeling, the finite element formulation and the perturbation technique are adopted to investigate the vibration response and instability behavior of the DWCNTs under electrostatic actuation. Note that both layers of the DWCNTs vibrate with the same frequency under the primary and secondary resonance conditions. The nonlinear vibration behaviors in both deterministic and stochastic cases are very similar to each other, except in the stochastic case, some statistical quantities such as the mean values and standard deviations of the displacements of DWCNTs must be considered and dealt with in the whole process.