The multiple-demand (MD) network serves as a core system for domain-general cognitive control, with robust activation with increased demand across diverse tasks. While fMRI studies have characterised the MD network's role in cognitive demand, linking these findings to electrophysiological activity remains a critical challenge. This article discusses the potential of oscillatory and aperiodic neural activity to bridge this gap. Although recent meta-analyses highlight mid-frontal theta power as a robust marker of task demand, its localised spatial distribution, limited cross-task generalisability, and potential confounds from aperiodic components limit its ability to fully represent the MD network. In contrast, aperiodic activity, particularly broadband power, has emerged as a strong candidate for indexing task demand due to its robust decoding performance and cross-task generalisability in response to diverse task demands, and spatial overlap with MD regions. Aperiodic activity may reflect fundamental neural properties, such as spiking rates and excitation/inhibition (E/I) balance, and is scale-free and exists across modalities, positioning it as a promising mechanism underpinning domain-general cognitive control that links to the MD network. Meanwhile, multiplexed low-frequency oscillations (e.g., delta and theta) may implement inter-regional synchronisation within the MD network, enabling large-scale coordination between MD subregions that supports cognitive control. Together, this article proposes a hypothetical framework linking the MD network to electrophysiological responses: Aperiodic broadband power, potentially reflecting population-level spiking activity, may support activation within MD regions, while multiplexed low-frequency oscillatory synchronisations may mediate inter-regional connectivity between MD regions.