Voluntarily directing visual attention to a cued position in space leads to improved processing of forthcoming visual stimuli at the attended position, and attenuated processing of competing stimuli elsewhere, due to anticipatory tuning of visual cortex activity. In EEG, recent evidence points to a determining role of modulations of posterior alpha-band activity (8-14 Hz) in such anticipatory facilitation (alpha-power decreases) versus inhibition (alpha-power increases). Yet, while such alpha-modulations are a common finding, the direction of modulation varies to a great extent across studies implying dependence on task demands. Here, we reveal opposite modulation of posterior alpha-power with early/initiation versus later/sustained processes of anticipatory attention orienting. Marked alpha-decreases were observed during shifting of attention (initial 700 ms) over occipito-parietal areas processing to-be-attended visual space, while alpha-increases dominated in the subsequent maintenance phase (>700 ms) over occipito-parietal cortex tuned to unattended positions. Notably, the presence of alpha-modulation strongly depended on individual resting alpha-power. Overall, this provides further support to an active facilitative versus inhibitory role of alpha-power decreases and increases and suggests that these attention-related changes are differentially deployed during anticipatory attention orienting to prepare versus maintain the cortex for optimal target processing.