This paper presents a model of spatiotemporal variations in a dynamic texture (DT) sequence. Most recent work on DT modelling represents images in a DT sequence as the responses of a linear dynamical system (LDS) to noise. Despite its merits, this model has limitations because it attempts to model temporal variations in pixel intensities which do not take advantage of global motion coherence. We propose a model that relates texture dynamics to the variation of the Fourier phase, which captures the relationships among the motions of all pixels (i.e. global motion) within the texture, as well as the appearance of the texture. Unlike LDS, our model does not require segmentation or cropping during the training stage, which allows it to handle DT sequences containing a static background. We test the performance of this model on recognition and synthesis of DT's. Experiments with a dataset that we have compiled demonstrate that our phase based model outperforms LDS.