In the atomic layer deposition (ALD) of cobalt (Co) and ruthenium (Ru) metals using nitrogen plasma, the structure and composition of the post N-plasma NHx-terminated (x = 1 or 2) metal surfaces are not well-known but are important in the subsequent metal-containing pulse. In this paper, we use the low-index (001) and (100) surfaces of Co and Ru as models of the metal polycrystalline thin films. The (001) surface with a hexagonal surface structure is the most stable surface, and the (100) surface with a zigzag structure is the least stable surface but has high reactivity. We investigate the stability of NH and NH2 terminations on these surfaces to determine the saturation coverage of NHx on Co and Ru. NH is most stable in the hollow hexagonal close-packed site on the (001) surface and the bridge site on the (100) surface, while NH2 prefers the bridge site on both (001) and (100) surfaces. The differential energy is calculated to find the saturation coverage of NH and NH2. We also present results on mixed NH/NH2-terminations. The results are analyzed by thermodynamics using Gibbs free energies (ΔG) to reveal temperature effects on the stability of NH and NH2 terminations. Ultra-high vacuum and standard ALD operating conditions are considered. Under typical ALD operating conditions, we find that the most stable NHx-terminated metal surfaces are 1 ML NH on the Ru(001) surface (350–550 K), 5/9 ML (0.56 ML) NH on the Co(001) surface (500–650 K) and a mixture of NH and NH2 on both Ru(100) and Co(100) surfaces.