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 .