Tracking moving objects is a vital visual task for the survival of an animal. We describe oscillatory neural network models of visual attention with a central element that can track a moving target among a set of distracters on the screen. At the initial stage, the model forms the focus of attention on an arbitrary object that is considered as a target. Other objects are treated as distracters. We present here two models: 1) synchronisation based model designed as a network of phase oscillators and 2) spiking neural model which is based on the idea of resource-limited parallel visual pointers. Selective attention and the tracking process are represented by the partial synchronisation between the central unit and a subgroup of peripheral elements. Simulation results are in overall agreement with the findings from psychological experiments: overlapping between the target and distractors is the main source of errors.