Abstarct: In this thesis, the nonlinear vibrations of axially moving viscoelastic nanobeams with axially functionally graded (AFG) properties are investigated. The equation of motion is derived using Hamilton's principle. Subsequently, the equation of motion is discretized using the Galerkin method. Analytical solutions are obtained using the method of multiple scales and parametric resonance for the cases of simply supported and clamped-simply supported boundary conditions. The natural frequency relation and the detuning parameter equation in terms of response amplitude are presented. Finally, the effects of damping, nonlocal parameters, mechanical property distribution, nanobeam speed, and boundary conditions on the system's response behavior are examined.