The mechanisms involved in degradation of the native protein structure was analyzed by comparing the temperature dependences of the hydrogen exchange (HE) and proteolytic cleavage rates of hen egg lysozyme (HEL), human hemoglobin (Hb), and its apoform (apoHb). Acceleration of the burstlike (all or none) proteolytic degradation of HEL in a high temperature range results from the intensification of global fluctuations with overal structure unfolding, indicated by HE. The rates of Hb and apoHb burstlike degradation and HE weakly depend on the temperature in the range where only local fluctuations of the native structure are detectable by HE. These two proteins are cleaved according to a self-accelerated burstlike mechanism with the initial rate-limiting single cleavage due to local fluctuations in the native structure. Such fluctuations play an important role in intracellular burstlike proteolytic degradation of native proteins.