In this article, the nonlinear parametric response of viscoelastic nanotubes conveying pulsatile flow is investigated. A two-parameter scale-dependent elasticity-based model is developed within the framework of a nonlocal theory with strain gradient influences. To model the effects of fluid molecules, which slip on the internal nanotube wall, on the parametric response, Karniadakis–Beskok approach is used. Viscoelastic effects are also described via Kelvin–Voigt scheme. Hamilton law, Galerkin and continuation techniques are, respectively, utilized in this analysis for obtaining, discretising and solving nonlinear coupled equations. Both subcritical and supercritical nonlinear parametric responses are examined considering various parameters such as the speed variation amplitude and frequency. The viscoelastic nanotube conveying pulsatile flow exhibits a hardening nonlinearity in the subcritical regime while it displays a softening nonlinearity in the supercritical regime.