We study the kinematic properties of dense gas surrounding massive protostars recognized by Bontemps et a. (2010) in a sample of five Massive Dense Cores in Cygnus-X. We investigate whether turbulent support plays a major role in stabilizing the core against fragmentation into Jeans-mass objects or alternatively, the observed kinematics could indicate a high level of dynamics. We present IRAM 30m single-dish (HCO+ and H13CO+) and IRAM PdBI high angular-resolution observations of dense gas tracers (H13CO+ and H13CN) to reveal the kinematics of molecular gas at scales from 0.03 to 0.1 pc. Radiative transfer modeling shows that H13CO+ is depleted within the envelopes of massive protostars and traces the bulk of material surrounding the protostars rather than their inner envelopes. H13CN shows a better correspondence with the peak of the continuum emission, possibly due to abundance anomalies and specific chemistry in the close vicinity of massive protostars. Analyzing the line-widths we show that the observed line-dispersion of H13CO+ at the scale of MDCs is smaller than expected from the quasi-static, turbulent-core model. At large-scales, global organized bulk motions are identified for 3 of the MDCs. At small-scales, several spectral components are identified in all MDCs showing filamentary structures and intrinsic velocity gradients towards the continuum peaks. The dynamics of these flows show diversity among the sample and we link this to the specific fragmentation properties of the MDCs. No clear evidence is found for a turbulence regulated, equilibrium scenario within the sample of MDCs. We propose a picture in which MDCs are not in equilibrium and their dynamics is governed by small-scale converging flows, which may initiate star-formation via their shears.< Réduire