A first order phase transition occurs at Ni (111) surfaces under conditions of controlled chemical potential. For a dilute Ni-C alloy of fixed bulk composition an abrupt change occurs (as temperature is lowered) in the surface carbon coverage from a very low coverage state to a two dimensional crystalline C overlayer. In the present work the possible effects of substrate orientation on the occurrence and characteristics of the transition have been investigated. On surfaces vicinal to (111) and on the (311) and (110) planes abrupt segregation of a graphitic monolayer was observed. The observed coverage-temperature relationship was similar to that for (111) with the monolayer formation occurring at a temperature between 10% and 12% higher than the equilibrium precipitation temperature. Surface reconstruction accompanies the monolayer condensation and precipitation processes. At dilute carbon coverages and high temperatures the vicinal planes have arrays of monoatomic height steps; upon monolayer formation rearrangement of the surface steps occurs to produce facets of (111) and (110) for surfaces along the  zone and of (111) and (311) for surfaces along the  zone. Qualitatively different behavior was observed with (100) and (210). Monolayer graphite condensation was also observed with both of the surfaces but the high temperature region was characterized by a gradually decreasing carbon coverage for which the Auger line shape was that of nickel carbide. Upon graphite precipitation at the solubility limit all surfaces become unstable with respect to formation of  facets.