  Using new accurate fundamental parameters of 30 Galactic A and F supergiants,
namely their effective temperatures Teff and surface gravities log g, we
implemented a non-LTE analysis of the nitrogen abundance in their atmospheres.
It is shown that the non-LTE corrections to the N abundances increase with
Teff. The nitrogen overabundance as a general feature of this type of stars is
confirmed. A majority of the stars has a nitrogen excess [N/Fe] between 0.2 and
0.9 dex with the maximum position of the star's distribution on [N/Fe] between
0.4 and 0.7 dex. The N excesses are discussed in light of predictions for
B-type main sequence (MS) stars with rotationally induced mixing and for their
next evolutionary phase, i.e. A- and F-type supergiants that have experienced
the first dredge-up. Rotationally induced mixing in the MS progenitors of the
supergiants may be a significant cause of the nitrogen excesses. When comparing
our results with predictions of the theory developed for stars with the mixing,
we find that the bulk of the supergiants (28 of 30) show the N enrichment that
can be expected (i) either after the MS phase for stars with the initial
rotational velocities v0 = 200-400 km s-1, (ii) or after the first dredge-up
for stars with v0 = 50-400 km s-1. The latter possibility is preferred on
account of the longer lifetime for stars on red-blue loops following the first
dredge-up. Two supergiants without a discernible N enrichment, namely HR 825
and HR 7876, may be post-MS objects with the relatively low initial rotational
velocity of about 100 km s-1. The suggested range for v0 is approximately
consistent with inferences from the observed projected rotational velocities of
B-type MS stars, progenitors of A and F supergiants.
