Search for Evolutionary Changes in the Periods of the Double-Mode Cepheid AS Cas

For both periods of the double-mode classical Cepheid AS Cas we have constructed $$O-C$$ diagrams spanning a time interval of 132 years. The $$O-C$$ diagrams have the shape of parabolas, which has allowed us for the first time to determine the quadratic light elements and to calculate the rates of evolutionary changes in their periods: $$dP_{0}/dt=+0.065({\pm}{0.010})$$ s yr $${}^{-1}$$ for the fundamental mode and $$dP_{1}/dt=+0.163({\pm}{0.006})$$ s yr $${}^{-1}$$ for the first overtone, in agreement with the theoretical calculations for the third crossing of the instability strip. The pulsation stability test proposed by Lombard and Koen has confirmed that the changes in the periods are real.