Neutron inelastic scattering investigations have been performed on the spin tetrahedral system Cu2Te2O5X2 (X=Cl,Br). We report the observation of magnetic excitations with a dispersive component in both compounds, associated with the three-dimensional incommensurate magnetic order that develops below TNCl=18.2K and TNBr=11.4K. The excitation in Cu2Te2O5Cl2 softens as the temperature approaches TNCl, leaving diffuse quasi-elastic scattering above the transition temperature. In the bromide, the excitations are present well above TNBr, which might be attributed to the presence of a degree of low dimensional correlations above TNBr in this compound. © 2005 The American Physical Society.