Everyday cognitive functioning is characterized by constant alternations between different modes of information processing, driven by fluctuations in environmental demands. At the neural level, this is realized through corresponding dynamic shifts in functional activation and network connectivity. A distinction is often made between the Default Mode Network (DMN) as a task-negative network that is upregulated in the absence of cognitive demands, and task-positive networks that are upregulated when cognitive demands such as attention and executive control are present. Such networks have been labelled the Extrinsic Mode Network (EMN). We investigated changes in brain activation and functional network connectivity during repeated alternations between levels of cognitive effort. Using fMRI and a block-design Stroop paradigm, participants switched back and forth between periods of no effort (resting), low effort (word reading, automatic processing) and high effort (color naming, cognitive control). Results showed expected EMN-activation for task versus rest, and likewise expected DMN-activation for rest versus task. The DMN was also more strongly activated during low effort contrasted with high effort, suggesting a gradual up- and down-regulation of the DMN, depending on the level of demand. The often reported anti-correlation between DMN and EMN was only present during periods of low effort, indicating intermittent contributions of both networks. These results challenge the traditional view of the DMN as solely a task-negative network. Instead, the present results suggest that both EMN and DMN may contribute to low-effort cognitive processing. In contrast, periods of resting and high effort are dominated by the DMN and EMN, respectively.