Effects associated with nonlocality of the electron energy distribution function (EEDF) in a bounded, low-temperature plasma containing fast electrons, can lead to a significant increase in the near-wall potential drop, leading to self-trapping of fast electrons in the plasma volume, even if the density of this group is only a small fraction (∼0.001%) of the total electron density. If self-trapping occurs, the fast electrons can substantially increase the rate of stepwise excitation, supply additional heating to slow electrons, and reduce their rate of diffusion cooling. Altering the source terms of these fast electrons will, therefore, alter the near-wall sheath and, through modification of the EEDF, a number of plasma parameters. Self-trapping of fast electrons is important in a variety of plasmas, including hollow-cathode discharges and capacitive rf discharges, and is especially pronounced in an afterglow plasma, which is a key phase of any pulse-modulated discharge. In the afterglow, the electron temperature is less than a few tenths of an electron volt, and the fast electrons will have energies typically greater than an electron volt. It is shown that in the afterglow plasma of noble gases, fast electrons, arising from Penning ionization of metastable atoms, can lead to the above condition and significantly change the plasma and sheath properties. Similar effects can be important in technologically relevant electronegative gas plasmas, where fast electrons can arise due to electron detachment in collisions of negative ions with atomic species. Both experimental and modeling results are presented to illustrate these effects.