Phanerozoic marine genera apparently do not become less extinction-prone with age. Higher extinction probability in "young" cohorts of genera is better explained by initially different levels of extinction-tolerance of genera in the cohort. This fact agrees with one of the two basic statements of the "Red Queen" hypothesis (Van Valen, 1973). In the second statement (the idea that the increase in fitness lowers extinction probability) the term "fitness" should be changed to "adaptability". The increase of extinction-tolerance, that can be interpreted as the increase of adaptability to unpredictable changes of environment, is found in succession of "generations" of genera that replace one another through time. This increase reveals itself, firstly, in the growth of mean duration of genera, as well as in the decrease of extinction/origination rates, gradual accumulation of long-lived genera and origination of genera with higher duration. The increase of adaptability may be caused by selective extinction of stenotopic, ecologically specialized forms; Cope's law; evolution of ecosystems that involves development of more effective mechanisms of sustaining homeostasis which may stimulate the recovery of a genus after partial extinction.