The kinetics is analyzed of the drift of non-potential plasma waves in spatial positions and wavevectors due to plasma's spatial inhomogeneity. The analysis is based on highly informative kinetic scenarios of the drift of electromagnetic waves in a cold ionized plasma in the absence of a magnetic field (Erofeev 2015 Phys. Plasmas 22 092302) and the drift of long Langmuir waves in a cold magnetized plasma (Erofeev 2019 J. Plasma Phys. 85 905850104). It is shown that the traditional concept of the wave kinetic equation does not account for the effects of the forced plasma oscillations that are excited when the waves propagate in an inhomogeneous plasma. Terms are highlighted that account for these oscillations in the kinetic equations of the above-mentioned highly informative wave drift scenarios.