The model of gas bubble growth in high-viscous gas-saturated magmatic melt, subjected to rapid decompression, is presented in the current study. It is shown that consideration of unsteady character of the process is extremely important in a wide range of supersaturation. The analytical solution is found for the profile of dissolved gas concentration and the rate of bubble growth. The model of kinetics of overall degassing is developed. This model is based on distinguishing the so-called "forbidden" zone in the melt volume with suppressed formation of the new nucleation sites. The simple analytical dependences of the number of nucleating bubbles and typical nucleation time on the value of initial decompression were derived together with time dependence of volumetric concentration of the gas phase. Our results match the available experimental data.