Key points The cortical mechanisms of grasping have been extensively studied in macaques and humans; here, we investigated whether common marmosets could rely on similar mechanisms despite strong differences in hand morphology and grip diversity. We recorded electrocorticographic activity over the sensorimotor cortex of two common marmosets during the execution of different grip types, which allowed us to study cortical activity (power spectrum) and physiologically inferred connectivity (phase‐slope index). Analyses were performed in beta (16–35 Hz) and gamma (75–100 Hz) frequency bands and our results showed that beta power varied depending on grip type, whereas gamma power displayed clear epoch‐related modulation. Strength and direction of inter‐area connectivity varied depending on grip type and epoch. These findings suggest that fundamental control mechanisms are conserved across primates and, in future research, marmosets could represent an adequate model to investigate primate brain mechanisms. Abstract The cortical mechanisms of grasping have been extensively studied in macaques and humans. Here, we investigated whether common marmosets could rely on similar mechanisms despite striking differences in manual dexterity. Two common marmosets were trained to grasp‐and‐pull three objects eliciting different hand configurations: whole‐hand, finger and scissor grips. The animals were then chronically implanted with 64‐channel electrocorticogram arrays positioned over the left premotor, primary motor and somatosensory cortex. Power spectra, reflecting predominantly cortical activity, and phase‐slope index, reflecting the direction of information flux, were studied in beta (16–35 Hz) and gamma (75–100 Hz) bands. Differences related to grip type, epoch (reach, grasp) and cortical area were statistically assessed. Results showed that whole‐hand and scissor grips triggered stronger beta desynchronization than finger grip. Task epochs clearly modulated gamma power, especially for finger and scissor grips. Considering effective connectivity, finger and scissor grips evoked stronger outflow from primary motor to premotor cortex, whereas whole‐hand grip displayed the opposite pattern. These findings suggest that fundamental control mechanisms, relying on adjustments of cortical activity and connectivity, are conserved across primates. Consistently, marmosets could represent a good model to investigate primate brain mechanisms.