While scanning our environment, the retinal image changes with every saccade. Nevertheless, the visual system anticipates where an attended target will be next and attention is updated to the new location. Recently, two different types of perisaccadic attentional updates were discovered: Predictive remapping of attention before saccade onset (Rolfs, Jonikaitis, Deubel, & Cavanagh, 2011) as well as lingering of attention after saccade (Golomb, Chun, & Mazer, 2008;Golomb, Pulido, Albrecht, Chun, & Mazer, 2010). We here propose a neurocomputational model located in LIP based on a previous model of perisaccadic space perception (Ziesche & Hamker, 2011. Our model can account for both types of updating of attention at a neural systems level. The lingering effect originates from the late updating of the proprioceptive eye position signal and the remapping from the early corollary discharge signal. We put these results in relationship to predictive remapping of receptive fields and show that both phenomena arise from the same simple, recurrent neural circuit. Thus, together with the previously published results, the model provides a comprehensive framework to discuss multiple experimental observations that occur around saccades.