Studying mu-rhythm in developmental disorders is crucial for identifying the origin of motor and social malfunctioning. However, the commonly used mu-rhythm experimental protocol, that requires following instructions, is challenging for children with motor and cognitive deficits. Here we present an inclusive experimental procedure that contains passive hand movement, closed and open eyes and hand movement observation and examine properties of EEG mu-rhythm obtained in this paradigm in 51 typically developing children and adults aged from 4 to 31 years. The independent component analysis (ICA) was used to separate occipital alpha- and mu-rhythm components and showed better performance than the channel-wise analysis. The identified mu-rhythm ICA components were localized above the left and right sensorimotor cortex, demonstrating suppression both to passive hand movement and hand movement observation and no difference in power between closed- and open-eye conditions. No interhemispheric differences were observed. The alpha-rhythm ICA components were localized in occipital regions and demonstrate characteristic suppression to open-eye conditions. The mu-rhythm frequency of peak suppression to passive hand movement as well as the amount of suppression increased with age. The beta-band mu-rhythm activity, while being less pronounced, was also suppressed both during passive hand movement and hand movement observation, while to a lesser degree than alpha-band mu during passive hand movement. Thus, we confirmed the classical properties of mu-rhythm and for the first time showed the developmental trajectory of mu-rhythm properties obtained during passive hand movement. The proposed experimental protocol and pipeline can be used further in studies of the mu-rhythm in challenging populations.