In the antisaccade paradigm subjects are instructed to perform eye movements in the opposite direction from the location of a visually appearing stimulus while they are fixating on a central stimulus. A recent study investigated saccade reaction times (SRTs) and percentages of erroneous prosaccades (towards the peripheral stimulus) of 2006 young men performing visually guided antisaccades. A unimodal distribution of SRTs (ranging from 80 to 600 ms) as well as an overall 25% of erroneous prosaccade responses was reported in that large sample. In this article, we present a neural model of saccade initiation based on competitive integration of planned and reactive saccade decision signals in the intermediate layer of the superior colliculus. In the model the decision processes grow nonlinearly towards a preset criterion level and when they cross it, a movement is initiated. The resultant model reproduced the unimodal distributions of SRTs for correct antisaccades and erroneous prosaccades as well as the variability of SRTs and the percentage of erroneous prosaccade responses.