The mechanism and kinetics of single-walled carbon nanotube (SWNT) nucleation from Fe- and Ni-carbide nanoparticle precursors have been investigated using quantum chemical molecular dynamics (QM/MD) methods. The dependence of the nucleation mechanism and its kinetics on environmental factors, including temperature and metal-carbide carbon concentration, has also been elucidated. It was observed that SWNT nucleation occurred via three distinct stages, viz. the precipitation of the carbon from the metal-carbide, the formation of a "surface/subsurface" carbide intermediate species, and finally the formation of a nascent sp(2)-hybidrized carbon structure supported by the metal catalyst. The SWNT cap nucleation mechanism itself was unaffected by carbon concentration and/or temperature. However, the kinetics of SWNT nucleation exhibited distinct dependences on these same factors. In particular, SWNT nucleation from Ni(x)C(y) nanoparticles proceeded more favorably compared to nucleation from Fe(x)C(y) nanoparticles. Although SWNT nucleation from Fe(x)C(y) and Ni(x)C(y) nanoparticle precursors occurred via an identical route, the ultimate outcomes of these processes also differed substantially. Explicitly, the Ni(x)-supported sp(2)-hybridized carbon structures tended to encapsulate the catalyst particle itself, whereas the Fe(x)-supported structures tended to form isolated SWNT cap structures on the catalyst surface. These differences in SWNT nucleation kinetics were attributed directly to the relative strengths of the metal-carbon interaction, which also dictates the precipitation of carbon from the nanoparticle bulk and the longevity of the resultant surface/subsurface carbide species. The stability of the surface/subsurface carbide was also influenced by the phase of the nanoparticle itself. The observations agree well with experimentally available data for SWNT growth on iron and nickel catalyst particles.