An oscillatory neural network model of multiple object tracking is described. The model works with a set of identical visual objects moving around the screen. At the initial stage, the model selects into the focus of attention a subset of objects initially marked as targets. Other objects are used as distractors. The model aims to preserve the initial separation between targets and distractors while objects are moving. This is achieved by a proper interplay of synchronizing and desynchronizing interactions in a multilayer network, where each layer is responsible for tracking a single target. The results of the model simulation are presented and compared with experimental data. In agreement with experimental evidence, simulations with a larger number of targets have shown higher error rates. Also, the functioning of the model in the case of temporarily overlapping objects is presented.