The Selective Tuning Model is a proposal for modelling visual attention in primates and humans. Although supported by significant biological evidence, it is not without its weaknesses. The main one addressed by this paper is that the levels of representation on which it was previously demonstrated (spatial Gaussian pyramids) were not biologically plausible. The motion domain was chosen because enough is known about motion processing to enable a reasonable attempt at defining the feedforward pyramid. The effort is unique because it seems that no past model presents a motion hierarchy plus attention to motion. We propose a neurally-inspired model of the primate visual motion system attempting to explain how a hierarchical feedforward network consisting of layers representing cortical areas V1, MT, MST, and 7a detects and classifies different kinds of motion patterns. The STM model is then integrated into this hierarchy demonstrating that successfully attending to motion patterns, results in localization and labelling of those patterns.