A flowing helium afterglow apparatus has been used to study thermal-energy electron exchange collisions between spin-polarized electrons and O\sb2 or NO molecules. Penning ionization of CO\sb2 by spin-polarized He(2\sp3S) metastable atoms is used to produce electrons which retain the spin orientation of the metastables, and which rapidly thermalize in the CO\sb2. The reactant gas (O\sb2 or NO), when introduced into the flowstream, causes a decrease in the electron spin-polarization. The electrons are then extracted from the flowtube for measurement of the polarization they retain. The rate constant for the reaction e\sp−(↑) + X → e\sp−(↓) + X can then be determined, given the amount of polarization decrease, reactant-gas density, and reaction time. The rates are found to be k(O\sb2) = (8 ± 3.5) x 10\sp−11 cm\sp3/sec and k(NO) = (9 ± 4) x 10\sp−11 cm\sp3/sec. An upper limit to the electron attachment rate for formation of an excited negative ion is derived from these measurements, and the contribution of exchange to the total scattering is discussed. In addition, a new, non-invasive technique for measuring electron-drift velocity in the flowtube is describe. Modifications of the afterglow apparatus and use of laser radiation for He(2\sp3S) spin-orientation enable it to produce an electron beam having moderate to high current and high spin polarization. Polarizations of 80% are achieved for currents up to 1μA, with 60% polarization retained at 25μA. This compares favorably with other polarized electron sources, making the afterglow apparatus a candidate for use as a beam source in high-energy electron accelerators.