The etching of silicon nitride (Si3N4) and silicon dioxide (SiO2) in the afterglow of NF3 and NF3/O-2 microwave discharges has been characterized. The etch rates of both materials increase approximately linearly with the flow of NF3 due to the increased availability of F atoms. The etch rate of Si3N4 is enhanced significantly upon O-2 injection into the NF3 discharge for O-2/NF3 ratios of 0.3 and higher, whereas the SiO2 etch rate is less influenced for the same flow ratios. X-ray photoelectron spectroscopy of processed Si3N4 samples shows that the fluorine content of the reactive layer, which forms on the Si3N4 surface during etching, decreases with the flow of O-2, and instead oxidation and nitrogen depletion of the surface occur. The oxidation of the reactive layer follows the same dependence on the flow of O-2 as the etch rate. Argon actinometry and quadrupole mass spectrometry are used to identify reactive species in the etching of both materials. The atomic fluorine density decreases due to dilution as O-2 is added to the discharge. The mass spectrometer did not detect NFx species (x = 1-3) at any discharge parameter setting, which indicates the near complete dissociation of NF,. Nitric oxide (NO) was detected by mass spectrometry, and the NO density shows the same dependence on O-2 how as the Si3N4 etch rate and the surface oxidation. Based on this observation, we propose that the etch rate enhancement for Si3N4 is due to the adsorption of the NO on the Si3N4 surface, followed by the formation of N-2 with a N atom from the surface. The O atom can then attach to the same surface site, contributing to the oxidation.