Introduction. Nonlinear EEG provides information about dynamic properties of the brain. This study aimed to compare nonlinear EEG parameters estimated from patients with Long COVID in different cognitive and motor tasks. Materials and Methods. This 12-month prospective cohort study included 83 patients with Long COVID: 53 symptomatic and 30 asymptomatic. Brain electrical activity was evaluated by EEG in 4 situations: (1) at rest, (2) during the Trail Making Test Part A (TMT-A), (3) during the TMT Part B (TMT-B), and (4) during a coordination task: the Box and Blocks Test (BBT). Nonlinear EEG parameters were estimated in the time domain (activity and complexity). Assessments were made at 0 to 3, 3 to 6, and 6 to 12 months after inclusion. Results. There was a decrease in activity and complexity during the TMT-A and TMT-B, and an increase of these parameters during the BBT in both groups. There was an increase in activity at rest and during the TMT-A in the COVID-19 group at 0 to 3 months compared to the control, an increase in activity in the TMT-B in the COVID-19 group at 3 to 6 months compared to the control, and reduced activity and complexity at rest and during the TMT-A at 6 to 12 months compared to the control. Conclusion. The tasks followed a pattern of increased activity and complexity in cognitive tasks, which decreased during the coordination task. It was also observed that an increase in activity at rest and during cognitive tasks in the early stages, and reduced activity and complexity at rest and during cognitive tasks in the late phases of Long COVID.