From the abundance study of a great quantity of luminosity type I and II supergiants we identified five first-crossing objects, which are rare massive stars evolving from their progenitors, main-sequence B stars, to red supergiants for the first time. Two of these first-crossing supergiants (HD 17905 and HD 172365) show abundances of Li, C, N, O, and Na that are completely unaltered by a mixing process of any kind, including the convective dredge up responsible for the CNO and NeNa anomalies observed for most of supergiants. The other three are in the process of such a dredge up (HD 18391, HD 32655, HD 159181). Three supergiants show the availability of lithium line and have strongly rotationally-broadened absorption lines. Two of these Li-rich supergiants — HD 17905 and HD 18391 — are reported for the first time in this study. The evolutionary status of all the five supergiants is discussed in detail and the conclusion is made that the mixing begins at effective temperatures of about 5800—6500 K , i.e., long before the red giant stage. Lithium is being destroyed first, followed by a gradual change in C, N, and Na abundances. We found however that in very fast rotators the destruction of lithium is inhibited, possibly, because the rotation-induced current circulation near the surface is sufficiently strong in this case to prevent lithium from reaching the top of convective zone and therefore from being dragged to deeper layers where temperature is sufficiently high for its destruction.