The formation of massive stars is a highly complex process in which it is unclear whether the star-forming gas is in global gravitational collapse or an equilibrium state supported by turbulence and/or magnetic fields. By studying the most massive and dense star-forming clump in the Galaxy at a distance of less than 3 kpc, i.e. the filament containing DR21 and DR21(OH), we obtained observational evidence to help us to discriminate between these two views. For that, we used molecular line data from our 13CO 1→0, CS 2→1, and N_2H^+ 1→0 survey of the Cygnus X region (FCRAO) and high-angular resolution observations in isotopomeric lines of CO, CS, HCO^+, N_2H^+, and H_2CO, obtained with the IRAM 30m telescope. The observations reveal a complex velocity field and velocity dispersion in which regions of the highest column-density, i.e. dense cores, have a lower velocity dispersion than the surrounding gas and velocity gradients that are not (only) due to rotation. Infall signatures in optically thick line profiles of HCO^+ and 12CO are observed along and across the whole DR21 filament. By modelling the observed spectra, we obtain a typical infall speed of ˜0.6 km s-1 and mass accretion rates of the order of a few 10-3 M_ȯ yr-1 for the two main clumps constituting the filament. These massive clumps (4900 and 3300 M_ȯ at densities of around 10^5 cm-3 within 1 pc diameter) are both gravitationally contracting (with free-fall times much shorter than sound crossing times and low virial parameter α). The more massive of the clumps, DR21(OH), is connected to a sub-filament, apparently 'falling' onto the clump. This filament runs parallel to the magnetic field. All observed kinematic features in the DR21 filament (velocity field, velocity dispersion, and infall), its filamentary morphology, and the existence of (a) sub-filament(s) can be explained if the DR21 filament was formed by the convergence of flows on large scales and is now in a state of global gravitational collapse. The observed velocity field and velocity dispersion are consistent with results from (magneto)-hydrodynamic simulations where the cores lie at the stagnation points of convergent turbulent flows.< Réduire