The multicomponent atmosphere of a comet with a complex-shaped nucleus has been simulated. The geometry and integral parameters of the gas productivity of the nucleus correspond to the conditions of comet 67P/Churyumov – Gerasimenko at the moment of its rendezvous with the Rosetta probe. The simulation was performed using both gas-dynamic methods, which involve numerical solution of the Euler/Navier – Stokes equations, and the kinetic approach based on the solution of the Boltzmann equation. The flow structure in the vicinity to the nucleus was analyzed, the applicability of gas-dynamic methods for prediction of a rarefied atmosphere was assessed, and the importance of considering translational-rotational nonequilibrium for interpreting observational data was analyzed.