The phenomenon of spontaneous bubble nucleation in extremely supersaturated (superheated) polymer-solvent systems has been studied experimentally. Spontaneous boiling-up temperatures T* for polystyrene and poly(ethylene glycol) solutions in a number of solvents have been measured at different values of pressure p and weight fraction of polymer c by the pulse heating method. The heating rate T varied from 10(5) to 10(7) K/s. For all systems studied, the values of T* have been found to increase with increasing p and c. The T*(p, c) dependence is discussed with the use of the data on the degree of compatibility of components. The peculiarities of polymeric solutions manifest themselves in the region c --> 1, as follows : (i) an abrupt increase (by 1-2 orders of magnitude) in the slope of the T*(c) dependence, and (ii) the appearance of the dependence of T* values on the heating rate. Our approach to the interpretation of this result assumes a change in the initial composition of a solution in the course of heating due to polymer decomposition. An example of the extended phase diagram of a polymer-solvent system including the kinetic surface of T*(p, c) is given.