Hyperspectral unmixing consists in determining the reference spectral signatures composing a hyperspectral image and their relative abundance fractions in each pixel. In practice, the identified signatures may be affected by a significant spectral variability resulting for instance from the temporal evolution of the imaged scene. This phenomenon can be accounted for by using a perturbed linear mixing model. This paper studies an online estimation algorithm for the parameters of this extended linear mixing model. This algorithm is of interest for the practical applications where the size of the hyper-spectral images precludes the use of batch procedures. The performance of the proposed method is evaluated on synthetic data.