Stability of radial and nonradial oscillations of massive supergiants is discussed. The kappa-mechanism and strange-mode instability excite oscillations having various periods in wide ranges of the upper part of the HR diagram. In addition, in very luminous (log L/L⊙ ≳ 5.9) models, monotonously unstable modes exist, which probably indicates the occurrence of optically thick winds. The instability boundary is not far from the Humphreys-Davidson limit. Furthermore, it is found that there exist low-degree (ℓ=1, 2) oscillatory convection modes associated with the Fe-opacity peak convection zone, and they can emerge to the stellar surface so that they are very likely observable in a considerable range in the HR diagram. The convection modes have periods similar to g-modes, and their growth-times are comparable to the periods. Theoretical predictions are compared with some of the supergiant variables.