This article deals with developing a coupled scale-dependent model to explore the nonlinear bifurcation response of initially imperfect nanotubes conveying nanofluid flow taking into consideration the influences of nonlinear viscoelasticity. Furthermore, the influences of both centrifugal and Coriolis forces are considered. The Beskok–Karniadakis model is employed to capture the influences of slip at the interface between the imperfect viscoelastic nanotube and the nanofluid. A refined combination of nonlocal and strain gradient elasticities is employed for taking into consideration size influences. After formulating the kinetic energy, elastic energy, viscous work and external work, the nonlinear coupled equations are derived for the nanofluid-conveying nanosystem, which simultaneously vibrates along the transverse and longitudinal directions. The nonlinear dynamical characteristics are calculated via utilising a Galerkin procedure and a direct-time-integration technique. It is found that chaotic regions can be removed by imposing a proper geometric imperfection.