Near-miscible gas injection represents a number of processes of great importance to reservoir engineers, including hydrocarbon gas injection and CO2 flood. Very little experimental data is available in the literature on displacements involving very low interfacial tension (IFT). In this paper, we present the results of a series of two- and three-phase gas injection (drainage) and oil injection (imbibition) core flood experiments for a gas/oil system at near-miscible (IFT = 0.04 mN m–1) conditions. Two different cores, a high-permeability (1000 mD) and a lower permeability (65 mD) core, were used in the experiments, and both water- and mixed-wet conditions were examined. The results show that, despite a very low gas/oil IFT, there is significant hysteresis between the imbibition and drainage oil and gas relative permeability (kr) curves in the 65 mD core. Hysteresis was less for the 1000 mD core (in comparison to the 65 mD core), but it still could not be ignored. Near-miscible kr hysteresis was significant for both water- and mixed-wet systems. The presence of immobile water in the water-wet cores improved oil relative permeabilities but reduced gas relative permeabilities in both imbibition and drainage directions. As a result, oil recovery for gas injection experiments improved when the rock contained immobile water. Both oil and gas relative permeabilities reduced when the rock wettability was altered to mixed-wet from water-wet, and as a result, oil recovery by gas injection in the mixed-wet rock was less than that obtained under water-wet conditions. We offer explanations for these observations based on our understanding of the pore-scale interactions and mechanisms, the distribution of fluid phases, and their spreading behavior. The results help us better understand the impact of some of the important parameters pertinent to kr and its hysteresis, especially in very low IFT gas/oil systems and mixed-wet rocks. Understanding these effects and behavior is important for the improved prediction of the performance of gas injection and water-alternating-gas (WAG) injection in oil reservoirs.