The approach described in the previous paper (Twu, C.H., Goon, J.E. and Cunningham, J.R., 1994a. A new generalized alpha function for a cubic equation of state. Part 1. Peng-Robinson equation. Fluid Phase Equilibria, 105 : 49-59) is applied to the Redlich-Kwong cubic equation of state (RK CEOS) to develop a new generalized alpha function for this equation. The new generalized alpha function for the RK CEOS reproduces the vapor pressure for hydrocarbons from the triple point to the critical point with almost identical accuracy to the generalized alpha function used for the Peng-Robinson CEOS in the previous paper. This indicates that the approach developed should be a general one, applicable to any cubic equation of state. The alpha function has been generalized in terms of the reduced temperature and acentric factor, so it can be used for any hydrocarbons and petroleum fractions, with no additional characterization to the standard methods required (Twu, 1984). The new alpha function is more appropriate for the RK CEOS than Soave’s alpha function, which has been widely used in phase behavior calculations in the petroleum production and refinery industries over the last twenty years.