High-temperature annealing is necessary in a number of applications for m-nitrides, including activation of Si+ or Mg+ implants for doping, maximization of implant-isolated regions, and Ohmic contact sintering. We have compared two methods for protection against surface dissociation of GaN, AlN, InN, InxGa1-xN, and InxAl1-xN during rapid thermal processing in N-2 ambients. In the first method, AlN or InN powder is placed in the reservoirs of a SiC-coated graphite susceptor and provides a N-2 overpressure for the nitride samples within the susceptor. In the second method, the nitrides are placed face down on other III-V substrates during annealing. In both techniques N loss from the nitride surface is found to occur at greater than or equal to 1050 degrees C for GaN and greater than or equal to 1100 degrees C for AlN and greater than or equal to InN, as measured by Auger electron spectroscopy. Real surface roughening is generally significant only for the In-containing materials, with GaN and AlN retaining smooth morphologies even up to 1150 degrees C unless H-2 is present in the annealing ambient. When InN powder is used in the susceptor, there is In droplet condensation on the surfaces of all samples above similar to 750 degrees C leading to higher root-mean-square surface roughness measured by atomic force microscopy. The N-2-deficient surfaces of the binary nitrides become strongly n type, while those of ternaries become less conducting. At temperature of 850-900 degrees C, the In droplets on thermally degraded ternaries also begin to evaporate, leading to an apparent improvement in morphology. The presence of H-2 or O-2 in the annealing ambient lowers the dissociation temperature of each of the nitrides by 100-200 degrees C, due to an enhancement in N-2 removal.