In this paper we apply a state-of-the-art algorithm for subspace identification of linear parameter-varying (LPV) systems to identify the coupled dynamics of the drive-train and the edgewise bending motion of the rotor blades of three-bladed wind turbines. These dynamics are varying with the rotor speed. The identification algorithm uses a factorization which makes it possible to form predictors based on past inputs, outputs, and the known rotor speed. The predictors contain the LPV equivalent of the Markov parameters. Using the predictors, ideas from Predictor Based Subspace IDentification (PBSID) were developed to estimate the state sequence from which the LPV system matrices can be constructed. The algorithm was applied not only to synthetic data generated by a computer simulation of a reference wind turbine, but also to data measured from the CART3 research wind turbine at the National Wind Technology Center of the National Renewable Energy Laboratory (NREL). This paper demonstrates that the linear time-varying behavior of the aeroelastic dynamics of the wind turbine rotor can be captured in an LPV model identified with measured input-output data.