Specially synthesized extra-large crystallites of zeolite LTA with intentionally added mesoporosity are used for an in-depth study of guest diffusion in hierarchical nanoporous materials by the pulsed field gradient NMR technique. Using propane as a guest molecule, intracrystalline mass transfer is demonstrated to be adequately described by a single effective diffusivity resulting from the weighted average of the diffusivities in the two (micro- and meso-) pore spaces. Gas-kinetic order-of-magnitude estimates of the diffusivities are in satisfactory agreement with the experimental data and are thus shown to provide a straightforward means for predicting and quantifying the benefit of hierarchically structured nanoporous materials in comparison with their purely microporous equivalent.