Density-dependent values of the electron drift velocity in hydrogen, deuterium, and nitrogen gas have recently been reported. Their reciprocal values are shown to be a linear function of the gas density. Several possible theoretical explanations are discussed, some of which lead to such a linear pressure dependence. It is concluded that electron trapping by some low-energy resonance states is likely to take place. "Rotational resonances" in atomrotator scattering have been described in a theoretical paper by Kouri, and it is thought that rotational resonances should be observed in electron-molecule scattering as well, at electron energies close to thermal energy. At the higher electron energies (~=1 eV), the known "single-particle" resonance states of H2 and N2 near 2 eV are probably responsible for the delay in the electron motion at high densities.