Posner and Petersen (1990) suggested that the attention system is composed of three networks: alerting, orienting, and executive functioning or control. Drawing on this theory, the Attentional Networks Test (ANT) was designed to quantify the functionality of the three attention networks. The ANT is used extensively in psychology, neuroscience, and medicine. Later adjustments of the ANT have demonstrated that the three attention networks do not operate independently and can interact. The current study examined whether such interactions are constant or result from task demands. In three experiments (N = 147) we measured alerting, orienting, executive control and their interactions while manipulating task demands. The interactions between the three networks differed between experiments, with no interactions detected in the third experiment. We conclude that the interactions between executive functioning and alertness, and between executive functioning and orienting depend on spatial processes and are not an innate feature of attention. Our results suggest that the three attention networks can function independently, depending on task demands. Our findings offer experimental support for Posner and Petersen's theory (1990) and suggest a novel way to optimize attention measurements.