  Aims. Having established the binary status of nineteen O-type stars located
in four Cygnus OB associations, we now determine their fundamental parameters
to constrain their properties and their evolutionary status. We also
investigate their surface nitrogen abundances, which we compare with other
results from the literature obtained for galactic O-type stars. Methods. Using
optical spectra collected for each object in our sample and some UV data from
the archives, we apply the CMFGEN atmosphere code to determine their main
properties. For the binary systems, we have disentangled the components to
obtain their individual spectra and investigate them as if they were single
stars. Results. We find that the distances of several presumably single O-type
stars seem poorly constrained because their luminosities are not in agreement
with the "standard" luminosities of stars with similar spectral types. The ages
of these O-type stars are all less than 7 Myrs. Therefore, the ages of these
stars agree with those, quoted in the literature, of the four associations,
except for CygOB8 for which the stars seem older than the association itself.
However, we point out that the distance of certain stars is debatable relative
to values found in the literature. The N content of these stars put in
perspective with N contents of several other galactic O-type stars seems to
draw the same five groups as found in the "Hunter" diagram for the O and B-type
stars in the LMC even though their locations are obviously different. We
determine mass-loss rates for several objects from the Halpha line and UV
spectra. Finally, we confirm the "mass discrepancy" especially for O stars with
masses smaller than 30 Msun. .
