While electroencephalogram (EEG) alpha desynchronization has been related to anticipatory orienting of visuospatial attention, an increase in alpha power has been associated to its inhibition. A separate line of findings indicated that alpha is affected by a deficient oxygenation of the brain or hypoxia, although leaving unclear whether the latter increases or decreases alpha synchronization. Here, we carried out an exploratory study on these issues by monitoring attention alerting, orienting, and control networks functionality by means of EEG recorded both in normoxia and hypoxia in college students engaged in four attentional cue-target conditions induced by a redesigned Attention Network Test. Alpha power was computed through Fast Fourier Transform. Regardless of brain oxygenation condition, alpha desynchronization was the highest during exogenous, uncued orienting of spatial attention, the lowest during alerting but spatially unpredictable, cued exogenous orienting of attention, and of intermediate level during validly cued endogenous orienting of attention, no matter the motor response workload demanded by the latter, especially over the left hemisphere. Hypoxia induced an increase in alpha power over the right-sided occipital and parietal scalp areas independent of attention cueing and conflict conditions. All in all, these findings prove that attention orienting is undergirded by alpha desynchronization and that alpha right-sided synchronization in hypoxia might sub-serve either the effort to sustain attention over time or an overall suppression of attention networks functionality.