An investigation is made into the dielectric properties of rare gas afterglow plasmas under varying conditions of pulsed discharge excitation in the pressure range 0·1-5 torr. Measurements are carried out in the frequency range 200-1500 MHz using a circular cylindrical cavity energized in the TM0m0 family of modes, the signal frequency increasing as m is increased. A study is made of the way in which the change in the cavity resonant radian signal frequency at a given time in the afterglow, (Δω)t, varies with m. Two kinds of afterglow are distinguished from experiment: those for which (Δω)t increases with increase in m, for example the afterglows following pulsed thermionic arc discharges, and those for which the sense of change of (Δω)t with m is reversed, for example afterglows following long-pulse (similar 11 ms), relatively low-power, radio-frequency discharges. At low pressures, and for a specific signal frequency, the second kind of afterglow causes the cavity to resonate at two different times during the decay; this does not happen with the first kind. Associated with the second kind are greatly increased afterglow decay rates which are dependent on the current pulse width δ. A change-over from the first to the second kind of afterglow is observed in xenon when the radio-frequency current pulse width is increased in the range 10 μs to 2 ms at fixed input power, or when the input power is increased in the range from about 200 w peak to about 1 kw peak at fixed δ. The phenomena are interpreted in terms of afterglows populated mainly by a free-electron gas (first kind), or mainly by a quasi-bound electron gas (second kind), or by a combined population of both gases (change-over regime). Measurements enable the plasma frequency and collision frequency for momentum transfer with neutral atoms to be determined for both kinds of afterglow and, in addition, determinations made of the internal frequency of oscillation of the quasi-bound electrons, yielding values for this parameter in the range 6 × 108-8 × 109 rad s-1.