MOF materials have recently emerged as viable candidate adsorbents for a number of different gases that are implicated in industrial processes. In this work, we present an exploration of the adsorption mechanism of CO2 and different alkanes (from C1 to C4) in the flexible MIL-53 (Cr) and its isostructural rigid form MIL-47(V). It is the first attempt to follow an “hybrid“ route based on the combination of Grand Canonical Monte Carlo and Molecular Dynamics simulations to capture the breathing of a MOF material along the adsorption process. This strategy relies on newly derived force field which successfully reproduces the structural switching between the narrow and the large pore versions of MIL-53(Cr) during the breathing phénomenom. We thus predict the adsorption isotherms and enthalpies of adsorption and probe the possible adsorption sites of the different adsorbates in both MIL materials. These results are then compared to those obtained using our preliminary approach which consisted of building “composite” isotherms and enthalpies from the contribution of both the narrow and large pore version of MIL-53(Cr)1. We will also report the adsorption behaviours for different CO2/alkane mixtures. All these simulations are then favorably compared to Microcalorimetry and in situ X-ray diffraction data. The diffusion of H2, CH4 and CO2 in both flexible MIL-53(Cr) and rigid MIL-47(V) systems has been also successfully characterized by combining QENS and Molecular Dynamics (MD) in MIL-53(Cr) and MIL-47 (V). Different loadings and temperatures were studied. In MIL-53(Cr), a 1D diffusion model for H2 was found to fit better the experimental spectra than the ordinary 3D one, leading to the observation for the first time of a 1D “supermobility” of H2 along the tunnel of the MIL materials with a self diffusivity Ds around 2.10-7 m2.s-1 at 77K2. Our simulations based on a small reparameterization of the existing forcefield for the H2/MIL framework, were in excellent agreement for both Ds as well as the activation energies. The Ds for CH4 was also successfully compared between experiment and simulation in the whole range of loading. Finally, the transport diffusivity Dt of CO2 in both large and narrow pore structures of MIL-53(Cr) was extracted from QENS and long MD runs since this molecule is a purely coherent scatterer.