This manuscript exploited a bottom to up modelling nano-mechanics theory to investigate the nonlinear stability and dynamic behaviors of perfect and imperfect carbon nanotubes (CNTs) in pre-buckling and post-buckling domains, for the first time. The Doublet Mechanics (DM) theory is exploited to induce the length scale of CNTs, micro-strain, and micro-stress effects, which are negligible in classical continuum theory. The Euler-Bernoulli kinematic and nonlinear mid-plane stretching effect are considered through analysis. The imperfection of CNTs is described by a harmonic function through spatial direction. The nonclassical sixth order nonlinear integro-partial-differential equation of CNTs is derived in detail. Based on the static equilibrium equation, analytical solutions for smallest buckling loads, as well as, nonlinear static response of perfect and imperfect CNTs in pre-buckling and post-buckling regimes are deduced. The equation of motion of linear vibration problem is solved analytically to get natural frequencies and corresponding mode shapes. Numerical studies investigate the impact of length scale parameter, imperfection amplitude and shear foundation constant on static and dynamic stabilities of CNTs with both fully clamped and simply supported conditions. The current model is effective in designing of NEMS, nano-sensor and nano-actuator manufactured by CNTs.