Higher brain functions depend upon the rapid creation and dissolution of ever changing synchronous cell assemblies. We examine the hypothesis that the dynamics of this process displays scale-free, self-similar properties. EEGs (19 channels, average reference, sample frequency 500 Hz) of 15 healthy subjects (10 men; mean age 22.5 years) were analyzed during eyes-closed and eyes-open no-task conditions. Mean level of synchronization as a function of time was estimated with the synchronization likelihood for five frequency bands (0.5-4, 4-8, 8-13, 13-30, and 30-48 Hz). Scaling in these time series was investigated with detrended fluctuation analysis (DFA). DFA analysis of global synchronization time series showed scale-free characteristics, suggesting neuronal dynamics do not necessarily have a characteristic time constant. The scaling exponent as determined with DFA differed significantly for different frequency bands and conditions. The exponent was close to 1.5 for low frequencies (delta, theta, and alpha) and close to 1 for beta and gamma bands. Eye opening decreased the exponent, in particular in alpha and beta bands. Fluctuations of EEG synchronization in delta, theta, alpha, beta, and gamma bands exhibit scale-free dynamics in eyes-closed as well as eyes-open no-task states. The decrease in the scaling exponent following eye opening reflects a relative preponderance of rapid fluctuations with respect to slow changes in the mean synchronization level. The existence of scaling suggests that the underlying dynamics may display self-organized criticality, possibly representing a near-optimal state for information processing.