  Pulsation period changes in Mira type variables are investigated using the
stellar evolution and nonlinear stellar pulsation calculations. We considered
the evolutionary sequence of stellar models with initial mass 3 Msol and
population I composition. Pulsations of stars in the early stage of the
asymptotic giant branch are shown to be due to instability of the fundamental
mode. In the later stage of evolution when the helium shell source becomes
thermally unstable the stellar oscillations arise in either the fundamental
mode (for the stellar luminosity L < 5.4e3 Lsol) or the first overtone (L > 7e3
Lsol). Excitation of pulsations is due to the kappa-mechanism in the hydrogen
ionization zone. Stars with intermediate luminosities 5.4e3 < L/Lsol < 7e3 were
found to be stable against radial oscillations. The pulsation period was
determined as a function of evolutionary time and period change rates \dot\Pi
were evaluated for the first ten helium flashes. The period change rate becomes
the largest in absolute value (\dot\Pi/\Pi\approx -0.01 per year) between the
helium flash and the maximum of the stellar luminosity. Period changes with
rate |\dot\Pi/\Pi| > 1e-3 per year take place during approx 500 years, that is
nearly one hundredth of the interval between helium flashes.
