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Neurons in the posterior parietal cortex of macaques show spatial tuning during several phases of an instructed delay reaching task, but their reference frames have been studied mostly during fixed periods without addressing how they evolve across task phases. In parietal area V6A, we reported recently that during the late delay and hand movement periods, most neurons represent target location either in body-centered frame of reference, or in mixed body/hand-centered coordinates, with no evidence of hand-centered representations. Here, we characterized the spatial representations of V6A neurons in earlier task epochs, i.e., immediately after target fixation and in the subsequent main part of the delay and examined whether the reference frames of individual neurons are stable across the task. We report no evidence of hand-centered coding also in the earlier phases of the task. Shortly, after target fixation and throughout the main part of the delay period, V6A neurons used either body-centered or mixed body/hand-centered reference frames. Most of the cells showed consistent reference frames across epochs. Interestingly, a population trend of shifting from mixed body/hand-centered frames to 'pure' body-centered coordinates was found as the task progressed. These findings suggest that, similar to other parietal areas, in V6A, the reference frames show a limited degree of temporal evolution. The stronger presence of mixed coding at the early task stages could reflect the early involvement of V6A in eye-hand coordination, whereas the increase in spatiotopic representations towards movement execution could be related to its role in online movement control.