The kinetic theory of degassing and swelling of a supersaturated-by-gas liquid solution under decompression has been formulated. The theory is based on the extended excluded volume approach to kinetics of gas-bubble nucleation. A description of the nucleation stage of supercritical gas-bubble formation with nonstationary nonuniform diffusion shells around the bubbles and mean-field mixing of the dissolved gas concentration at outer parts of the shells due to their stochastic overlapping has been built. In this way, the theory embraces the cases with any degree of initial gas supersaturation and deviation from the steady-state diffusion. It has been shown that the effects of nonstationary diffusion may be very significant in the growth of bubbles and, in particular, are responsible for a significant swelling of a supersaturated-by-gas liquid solution. Distribution of supercritical bubbles in sizes and gas concentration profiles at any moment of the nucleation stage as well as duration of the nucleation stage