Abstarct: Inimitable properties of graphene sheets enable a variety of applications such as axially moving nanodevices. Axially velocity affects dynamical response of systems. In this study linear vibration of an axially moving two-laxyer graphene nonoribbon with interlaxyer shear effect is proposed using nonlocal elasticity theory. baxsed on this theory stress at a point is a function of strain at all other points of the body. Euler-Bernoulli theory is used to model the system due to nanoribbon thickness and length. It is assumed that the laxyers have the same transverse displacement and curvature and there is no transverse separation between laxyers surfaces. A shear modulus is imported in the potential energy exxpression in order to consider the interlaxyer shear effect due to weak Van der Waals forces. Governing equations are obtained using Hamilton’s principle and are solved by Galerkin approach. As the system experience a coriolis acceleration component which renders the system gyroscopic, it is nonconservative and we have complex natural frequencies. Results for pinned-pinned and clamped-free boundary conditions are presented and compared to other available studies. It is observed that increasing axial velocity causes divergence and flutter instabilities in the system. Effects of different shear modulus and nonlocal parameter on critical speeds are also proposed. With the rapid technology developments in recent years, the serious request for miniaturized sensors has motivated developments of new classes of sensors with higher efficiencies in nanoscale size. These nano scale sensors are used in many applications such as ultra-sensitive mass detections and early diagnosis of dangerous diseases. Generally, different methods are used in literature to design and analyze nano- resonators, vibration baxsed methods and wave propagations baxsed methods. The detection principle baxsed on vibration or wave propagations analysis is to detect the recognizable shift in resonant frequencies or wave velocities in the nano-sensors induced by attachment of foreign atoms or molecules on surface of the sensors. The effect of moving speed, lumped mass weight and its position on vibration and instability of system are proposed. The results show that the natural frequencies of the system decrease with the increasing of the axially moving speed and mass weight, and the first natural frequency gets the minimum value when the mass is located at the midpoint of the beam. Effects of mass weight and it location on the divergence and flutter critical speeds are also investigated. In the last section of the paper, in order to take into account the geometric non-linearity due to large amplitude, the Lagrangian strain is used to obtain nonlinear equation of motion and non-zero equilibrium points are studied.