The dynamics of countercurrent transport of binary and ternary gas mixtures through a porous medium accompanied by a spontaneous temporary build-up of pressure inside the porous medium was experimentally studied. From the measurements, it follows that if a lighter gas replaces a heavier gas the pressure increases and vice versa. The larger the difference between molecular weights of the transported gases the larger the change of the pressure. The spontaneous pressure build-up can be satisfactorily described by the Mean Transport Pore Model (MTPM) or the Dusty Gas Model (DGM). Both models contain three parameters (transport parameters), which represent material constants of the porous medium, i.e., are independent of the kind of transported gases and conditions under which the transport takes place (temperature, pressure). Transport parameters have to be determined experimentally, e.g., by measurements similar to those performed in this study. With the use of obtained transport parameters it is possible to predict the transport under different conditions.