Relative permeabilities for three-phase flow are commonly predicted from two-phase-flow measurements using empirical models. These empirical models are usually tested against available steady-state data. However, the oil flow is transient during various production stages [e.g., gas injection after waterflood and steam-assisted gravity drainage (SAGD)]. Hence, there is a need to test the empirical models against unsteady-state or transient data. We compare two sets of three-phase oil-permeability data measured during tertiary gasflood. The first data set, which was recently published (Dehghanpour et al. 2011a), is measured during transient gravity-drainage experiments, and will be detailed further here. The second set was measured by Oak et al. (1990) during steady-state corefloods. We compare the two data sets with the corresponding two-phase permeability curves, and observe different qualitative behaviours. The comparison indicates that during steady-state tertiary gasflood, the presence and flow of water restrict the oil flow, while during transient tertiary gasflood, water-saturation drop enhances the oil flow. We test the performance of well-known empirical models further in predicting the two data sets, and explain how Stone I and saturation-weighted interpolation (SWI) should be used to usefully predict oil permeability during a three-phase tertiary displacement.