  Instability of population I (X=0.7, Y=0.02) massive stars against radial
oscillations during the post-main sequence gravitational contraction of the
helium core is investigated. Initial stellar masses are in the range from
65M_\odot to 90M_\odot. In hydrodynamic computations of self-exciting stellar
oscillations we assumed that energy transfer in the envelope of the pulsating
star is due to radiative heat conduction and convection. The convective heat
transfer was treated in the framework of the theory of time-dependent turbulent
convection. During evolutionary expansion of outer layers after hydrogen
exhaustion in the stellar core the star is shown to be unstable against radial
oscillations while its effective temperature is Teff > 6700K for
Mzams=65M_\odot and Teff > 7200K for mzams=90M_\odot. Pulsational instability
is due to the \kappa-mechanism in helium ionization zones and at lower
effective temperature oscillations decay because of significantly increasing
convection. The upper limit of the period of radial pulsations on this stage of
evolution does not exceed 200 day. Radial oscillations of the hypergiant resume
during evolutionary contraction of outer layers when the effective temperature
is Teff > 7300K for Mzams=65M_\odot and Teff > 7600K for Mzams=90M_\odot.
Initially radial oscillations are due to instability of the first overtone and
transition to fundamental mode pulsations takes place at higher effective
temperatures (Teff > 7700K for Mzams=65M_\odot and Teff > 8200K for
Mzams=90M_\odot). The upper limit of the period of radial oscillations of
evolving blueward yellow hypergiants does not exceed 130 day. Thus, yellow
hypergiants are stable against radial stellar pulsations during the major part
of their evolutionary stage.
