This paper contains a theoretical and experimental investigation of the flow in the vaneless and semi-vaneless space of a transonic radial compressor diffuser, especially for working points corresponding to the mass flow below choking values, in the efficient operating regimes. A type-dependent finite difference calculation has been developed for the inviscid flow. This method has been combined with a shock-boundary layer-interaction theory, which allows a more realistic calculation of the velocity distribution, taking into account the boundary layer variation along the sidewalls. In parallel with this analytical study, several diffuser geometries were also performance tested. A special data-reduction program allowed calculation of the throat blockage and the velocity distribution throughout the diffuser based on static and total pressure measurements. Schlieren pictures were also taken in order to have a better insight in the real flow phenomena at the diffuser entrance. From this experimental data, a detailed comparison with the analytical study was made. This combined theoretical and experimental study made it possible to show the influence of the geometrical parameters of the vaneless and semi-vaneless space on the velocity distribution, and on the throat blockage. Together with the data available in literature for channel diffusers, it allows a better prediction of the overall performances of diffuser systems.