Effective teams are essential for optimally functioning societies. However, little is known regarding the neural basis of two or more individuals engaging cooperatively in real-world tasks, such as in operational training environments. In this exploratory study, we recruited forty individuals paired as twenty dyads and recorded dual-EEG at rest and during realistic training scenarios of increasing complexity using virtual simulation systems. We estimated markers of intrinsic brain activity (i.e., individual alpha frequency and aperiodic activity), as well as task-related theta and alpha oscillations. Using nonlinear modelling and a logistic regression machine learning model, we found that resting-state EEG predicts performance and can also reliably differentiate between members within a dyad. Task-related theta and alpha activity during easy training tasks predicted later performance on complex training to a greater extent than prior behaviour. These findings complement laboratory-based research on both oscillatory and aperiodic activity in higher-order cognition and provide evidence that theta and alpha activity play a critical role in complex task performance in team environments.