  A massive star can enter the blue supergiant region either evolving directly
from the main-sequence, or evolving from a previous red supergiant stage. The
fractions of the blue supergiants having different histories depend on the
internal mixing and mass-loss during the red supergiant stage. We study the
possibility to use diagnostics based on stellar pulsation to discriminate blue
supergiants having different evolution histories. For this purpose we have
studied the pulsation property of massive star models calculated with the
Geneva stellar evolution code for initial masses ranging from 8 to 50 M$_\odot$
with a solar metallicity of $Z=0.014$. We have found that radial pulsations are
excited in the blue-supergiant region only in the models that had been
red-supergiants before. This would provide us with a useful mean to diagnose
the history of evolution of each blue-supergiant. At a given effective
temperature, much more nonradial pulsations are excited in the model after the
red-supergiant stage than in the model evolving towards the red-supergiant. The
properties of radial and nonradial pulsations in blue supergiants are
discussed. Predicted periods are compared with period ranges observed in some
\alpha-Cygni variables in the Galaxy and NGC 300. We have found that blue
supergiant models after the red-supergiant stage roughly agree with observed
period ranges in most cases. However, we are left with the puzzle that the
predicted surface N/C and N/O ratios seem to be too high compared with those of
Deneb and Rigel.
