Pulsations in B-type supergiants with masses $M<20M_\odot$ before and after core helium ignition

Evolutionary tracks and pulsational analysis of models with masses of 13-18 $M_\odot$ are presented. We address two important questions. The first one deals with one of the most unresolved problems in astrophysics, i.e., the existence of a blue loop after core helium ignition; the so called "to loop or not to loop" problem. We show that inward overshooting from the outer convective zone in the red giant phase is prerequisite for the development of the blue loop. Our second question concerns pulsational instability of models in the core helium burning phase. We present for the first time that models on the blue loop can have unstable modes driven by the $\kappa$ mechanism operating in the $Z-$bump. Contrary to post-main sequence models in the shell hydrogen burning phases, pulsational instability of the blue loop models depends mainly on effective temperature and metallicity is of secondary importance. Finally, we try to interpret the oscillation spectrum of the blue supergiant HD 163899, the only member of the SPBsg class, and to get some clue on the evolutionary status of the star.