[en] We analyze the temporal evolution of the population of ultracold polar molecules in a microwave (mw) field with a circular polarization. The molecules are in their ground ${}^1\mathrm{\Sigma <!--\; ??\; -->}$ state and treated as rigid rotors with a permanent dipole moment which interact with each other via the dipole–dipole (DD) interaction V_dd. The mw field mixes states with different quantum and photon numbers and the collisional dynamics in the mw field is mostly controlled by the ratios of the mw field frequency versus the rotational constant, and mw field Rabi frequency versus the rotational constant. There exists a special scattering process which is elastic by nature and due to a rotational energy exchange between the ground and the first excited rotational states. To analyze dynamics of polar molecules system in the mw field the equation of motion for the bare and dressed states is solved under different mw field parameters and molecular gas characteristics. Depending on the ratio of the Rabi frequency of a mw field and the magnitude of the DD interaction, beatings and oscillations occur in the bare and dressed states time-development. At a certain relation between the magnitudes of the mw detuning δ and the DD interaction $\mathrm{\delta <!--\; ??\; -->}=\pm <!--\; ??\; -->V_{\mathrm{d}\mathrm{d}}$, peak structures appear in the population of the excited bare state. Each peak is associated with an avoided crossing between the dressed states adiabatic curves at the same position of mw detuning. (paper)