Accurate determination of relative permeability values and their hysteresis is crucial for obtaining a reliable prediction of the: performance of water-alternating-gas (WAG) injection in oil reservoirs. In this paper, we report two series of gas/oil relative permeability curves obtained from coreflood experiments carried out in a mixed-wet core under a very low oil/gas interfacial tension (IFT) of 0.04 mN.m(-1). The first set of the corefloods began by gas injection (drainage) in the core saturated with oil and immobile water (S-wi). This was followed by a period of oil injection (imbibition), and this sequential injection of gas and oil continued, and in total, three drainage and two imbibition periods were carried out. In the second series of experiments, the core was initially saturated with gas and immobile water, and the experiment started with oil injection and followed by cycles of drainage and imbibitions. The measured pressure drop and production data were history matched through simulation analysis to obtain k(rg) and k(ro) values for each of the imbibition and drainage cycles. The results show that both the oil and the gas relative permeability curves show cycle-dependent hysteresis despite the very low gas/oil IFT. Therefore, the current assumption in existing models (such as Land, Carlson, and Killough) that the drainage scanning k(r) curves follow the preceding imbibition curve is not supported by our coreflood experiments. When compared to our measured data, the Carlson model predictions for k(rg) in imbibition direction are poor. The Killough model predictions underestimate k(rg) and overestimate k(ro), especially near trapped gas saturation regions. Beattie et al. hysteresis model is able to capture the k(rg) and k(ro) behavior that we observed in our experiments qualitatively, but it is still unable to predict the value of the observed hysteresis. The results suggest that, for mixed-wet systems, it is necessary to consider irreversible hysteresis loops for both the wetting and nonwetting phases. Such capability currently does not exist in reservoir simulators because of a lack of appropriate predictive tools.