Abstract. We consider series of tilted current sheet crossings, corresponding to flapping waves in the near-Earth magnetotail. We analyse Cluster observations from 2005 to 2009, when spacecraft visited the magnetotail neutral plane near X ∈ [−17, −8], Y ∈ [−16, −2] R E (in the GSM system). Large separation of spacecraft allows us to estimate both local and global properties of flapping current sheets. We find significant variation in flapping wave direction of propagation between the middle tail and flanks. Th series of tilted current sheets represent the system of periodic, almost parallel currents with typical thickness of current filaments about L = 0.4 R E . The earthward gradients of B z magnetic field are reduced within this current system in comparison with the gradients in the quiet near-Earth magnetotail. The wavelength (i.e. a distance between two crossings of current sheets with the same orientations) of the flapping waves is larger than 2π L for most of observations. The velocity of flapping wave propagation is about ion bulk velocity and is significantly lower than the velocity of ion drift relative to electrons. We discuss possible drivers of flapping and estimate the amplitude of the total parallel current generated by flapping waves.