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Separable visual attention functions are assumed to rely on distinct but interacting neural mechanisms. Bundesen's "theory of visual attention" (TVA) allows the mathematical estimation of independent parameters that characterize individuals' visual attentional capacity (i.e., visual processing speed and visual short-term memory storage capacity) and selectivity functions (i.e., top-down control and spatial laterality). However, it is unclear whether these parameters distinctively map onto different brain networks obtained from intrinsic functional connectivity, which organizes slowly fluctuating ongoing brain activity. In our study, 31 demographically homogeneous healthy young participants performed whole- and partial-report tasks and underwent resting-state functional magnetic resonance imaging (rs-fMRI). Report accuracy was modeled using TVA to estimate, individually, the four TVA parameters. Networks encompassing cortical areas relevant for visual attention were derived from independent component analysis of rs-fMRI data: visual, executive control, right and left frontoparietal, and ventral and dorsal attention networks. Two TVA parameters were mapped on particular functional networks. First, participants with higher (vs. lower) visual processing speed showed lower functional connectivity within the ventral attention network. Second, participants with more (vs. less) efficient top-down control showed higher functional connectivity within the dorsal attention network and lower functional connectivity within the visual network. Additionally, higher performance was associated with higher functional connectivity between networks: specifically, between the ventral attention and right frontoparietal networks for visual processing speed, and between the visual and executive control networks for top-down control. The higher inter-network functional connectivity was related to lower intra-network connectivity. These results demonstrate that separable visual attention parameters that are assumed to constitute relatively stable traits correspond distinctly to the functional connectivity both within and between particular functional networks. This implies that individual differences in basic attention functions are represented by differences in the coherence of slowly fluctuating brain activity.