In this article, for the first time, a coupled nonlinear model incorporating scale influences is presented to simultaneously investigate the influences of viscoelasticity and geometrical imperfections on the nonlocal coupled mechanics of carbon nanotubes; large deformations, stress nonlocality and strain gradients are captured in the model. The Kelvin-Voigt model is also applied in order to ascertain the viscoelasticity effects on the mechanics of the initially imperfect nanoscale system. The modified coupled equations of motion are then derived via the Hamilton principle. A solution approach for the derived coupled equations is finally developed applying a decomposition-based procedure in conjunction with a continuation-based scheme. The significance of many parameters such as size parameters, initial imperfections, excitation parameters and linear and nonlinear damping effects in the nonlinear mechanical response of the initially imperfect viscoelastic carbon nanotube is assessed. The present results can be useful for nanoscale devices using carbon nanotubes since the viscoelasticity and geometrical imperfection are simultaneously included in the proposed model.