We present a hierarchical neurodynamical system for object recognition based on attentional control of the spatial resolution with which an object is analyzed during an iterative hypothesis testing cycle. Psychophysical evidence strongly suggests that attentional processing results in the enhancement of the spatial resolution in the input region corresponding to the focus of attention. We adopt a computational neuroscience approach in order to analyze this attentional enhancement of the spatial resolution for object recognition. The system consists of a where- and a what-module which include networks with feedforward and feedback interconnections describing the mutual links between different areas of the visual cortex.