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Evolutionary tracks from the zero age main sequence to the asymptotic giantbranch were computed for stars with initial masses 2M_\odot <= Mzams <=5M_\odot and metallicity Z=0.02. Some models of evolutionary sequences wereused as initial conditions for equations of radiation hydrodynamics andturbulent convection describing radial stellar pulsations. The early asymptoticgiant branch stars are shown to pulsate in the fundamental mode with periodsfrom 30 to 400 day. The rate of period change gradually increases as the starevolves but is too small to be detected (d ln P/dt < 1.e-5 yr^-1). Pulsationproperties of thermally pulsing AGB stars are investigated on time intervalscomprising 17 thermal pulses for evolutionary sequences with intial massesMzams=2M_\odot and 3M_\odot and 6 thermal pulses for Mzams=4M_\odot and5M_\odot. TP-AGB stars with initial masses Mzams<=3M_\odot pulsate either inthe fundamental mode or in the first overtone, whereas more massive red giants(Mzams>=4M_\odot) pulsate in the fundamental mode with periods as long as 1.e3day. Most rapid pulsation period change with rate -0.02 < d ln P/dt < -0.01yr^-1 occurs during decrease of the surface luminosity after the maximum heliumluminosity. The rate of subsequent increase of the period is d ln P/dt <= 5.e-3yr^-1.

Pulsations of intermediate-mass stars on the asymptotic giant branch