A new experimental technique has been utilized for the measurement of rate constants for two- and three-body electron-attachment reactions. This technique is based on the observation of positive-ion and/or negative-ion decay(s) in a stationary afterglow. The transition of the decay from positive-ion electron ambipolar-diffusion domination at early times to positive-ion-negative-ion ambipolar-diffusion domination at late times is related to the disappearance of electrons from the decaying plasma. The time of occurrence of the transition in the afterglow is used to relate the attachment rate constants to other experimental observables. The two-body rate constant k2 for attachment to NO2 is determined to be 1.4+2.0-0.9 × 10-11 cm3/sec; similarly, the three-body rate constant k3 for attachment to NO is (6.8 +/- 3.4) × 10-32 cm6/sec, both at 296°K. The only negative ion observed in this study is NO-2, even under conditions in which three-body attachment in NO dominates the electron-loss processes; the absence of NO- under these conditions is investigated.