In recent years, the study and interpretation of mislocalization phenomena observed with moving objects have caused an intense debate about the processing mechanisms underlying the encoding of position. We use a neurophysiologically plausible recurrent network model to explain visual illusions that occur at the start, midposition, and end of motion trajectories known as the Fröhlich, the flash-lag, and the representational momentum effect, respectively. The model implements the idea that trajectories are internally represented by a traveling activity wave in position space, which is essentially shaped by local feedback loops within pools of neurons. We first use experimentally observed trajectory representations in the primary visual cortex of cat to adjust the spatial ranges of lateral interactions in the model. We then show that the readout of the activity profile at adequate points in time during the build-up, midphase, and decay of the wave qualitatively and quantitatively explain the known dependence of the mislocalization errors on stimulus attributes such as contrast and speed. We conclude that cooperative mechanisms within the network may be responsible for the three illusions, with a possible intervention of top-down influences that modulate the efficacy of the lateral interactions.