Previous studies that made use of basin models have shown that the normal geological evolution of the Paris basin does not generate the observed, albeit weak, excess pressures in some shale layers of the basin. Other processes that may have created the overpressures, currently neglected in such models, are investigated here. Terms accounting for osmotic effects and tectonic stress changes are successively added to the diffusivity equation. The effect of changes in outcrop boundary conditions is also calculated with a pseudo-two-dimensional analytical solution. These solutions are applied to the Callovo-Oxfordian shale formation in the eastern part of the Paris basin, France. It is shown that a long-term transient osmotic effect starting in the Tertiary could explain in part the observed excess pressures in the Callovo-Oxfordian shale assuming effective diffusion coefficients of 1--5 ¿ 10-12 m2 s-1 in line with the measurements and a pore radius b around 20 ¿ for the shales. However, because of the uncertainty on the value of the shale pore radius, additional head measurements and osmotic experiments on samples should be made to fully establish the possibility of an osmotic process. Our study also shows that recent changes in hydrodynamic boundary conditions could also explain excess pressure distribution in this shale layer. It is plausible that a combination of the two processes could best explain the distribution and intensity of the overpressures. Tectonic stress changes do not appear to be important; it is shown that for such processes, to maintain high pressures, strong and recent increase in tectonic compressive stress would be required.