Following an earlier investigation of Ledoux, the coefficient of pulsational stability has been recomputed for massive stars on the basis of the detailed models just published. From the homogeneous models representing the initial main-sequence state it is found that (assuming a helium content of 22 per cent) stars are pulsationally stable if they are lighter than 60 solar masses and unstable if they are heavier than this critical mass. From the inhomogeneous models representing subsequent evolution phases it is found that a star gains in pulsational stability as it evolves. For stars just above the critical mass, in the range from 60 to 65 solar masses, pulsational stability is gained so quickly after the initial main-sequence state that the pulsational instability can hardly have serious consequences. For stars heavier than 65 solar masses, however, the instability is of sufficient duration and e-folding speed to have probably major effects. As already suggested by Ledoux, the existence of a critical mass for pulsational stability of mainsequence stars makes it appear probable that pulsational instability is indeed the mechanism which determines the upper limit for stellar masses. To bridge the gap between the theoretical value of 65 solar masses and the observed limit of about 95 solar masses, one might assume that in this mass range the pulsational instability, though not yet strong enough to cause immediate disruption, is already sufficiently strong to cause continuous shell ejection, as indicated by the P Cygni phenomenon.