A methodology is presented to obtain the nonlinear aeroelastic response of horizontal axis wind turbines using accurate and computationally efficient aerodynamic and structural descriptions. For computing the geometrically nonlinear deformations of the rotor blades, we employ Simo-Vu-Quoc's geometrically exact finite-strain spatial rod model, which treats the displacements of the beam reference line and the rotations of the cross-section as configuration variables, without any restrictions on their magnitudes or those of the resulting 1-D strain measures. The structural description is Lagrangian, obviating the need for an explicit definition of centrifugal/coriolis forces. Towards the aerodynamic side, Blade Element Momentum Theory enhanced with several important corrections is employed, along with a dynamic stall model that accounts for the unsteady effects. A comprehensive treatment of the aeroelastic computations within the restrictions imposed by the aerodynamic theory is presented with the aid of a ‘shadow’ frame of reference rotating rigidly with the deforming blades. A novel strategy ‘primes’ the aeroelastic solver by moderating the response of rotor in its acceleration phase. An integrated MATLAB tool WindGEAR incorporating the two coupled codes is developed to simulate the fully-coupled aeroelastic response of the NREL 5 MW wind turbine. The results, when compared with published data, establish WindGEAR firmly as a robust wind turbine nonlinear aeroelastic analysis tool in time-domain. © 2018 Elsevier Inc.