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Aims. Having established the binary status of nineteen O-type stars locatedin four Cygnus OB associations, we now determine their fundamental parametersto constrain their properties and their evolutionary status. We alsoinvestigate their surface nitrogen abundances, which we compare with otherresults from the literature obtained for galactic O-type stars. Methods. Usingoptical spectra collected for each object in our sample and some UV data fromthe archives, we apply the CMFGEN atmosphere code to determine their mainproperties. For the binary systems, we have disentangled the components toobtain their individual spectra and investigate them as if they were singlestars. Results. We find that the distances of several presumably single O-typestars seem poorly constrained because their luminosities are not in agreementwith the "standard" luminosities of stars with similar spectral types. The agesof these O-type stars are all less than 7 Myrs. Therefore, the ages of thesestars 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 relativeto values found in the literature. The N content of these stars put inperspective with N contents of several other galactic O-type stars seems todraw the same five groups as found in the "Hunter" diagram for the O and B-typestars in the LMC even though their locations are obviously different. Wedetermine mass-loss rates for several objects from the Halpha line and UVspectra. Finally, we confirm the "mass discrepancy" especially for O stars withmasses smaller than 30 Msun. .

A spectroscopic investigation of the O-type star population in four Cygnus OB associations. II. Determination of the fundamental parameters