The quark-gluon-string model, based on the 1/N/sub f/ expansion of the amplitudes in QCD, is applied to processes of production of charmed D(D-bar) mesons and ..lambda../sub c/ baryons. It is shown that this model makes it possible to describe quantitatively the principal characteristics of the inclusive production of charmed particles. The experimental data indicate that the intercept of the psi Regge trajectory is ..cap alpha../sub psi/(0)approx. =0, and that the psi trajectory is nonlinear. Predictions are given for the inclusive spectra of charmed particles in a wide range of energies.