Studies on stress sensitivity of relative permeability in the laboratory were mostly carried out by varying overburden pressure at constant pore pressure (PP). However, in a real oilfield situation, changes in net stress are induced by changes in PP rather than overburden pressure. This research presents the effect of PP variation at a confining stress of 25 MPa on water-oil and silica nanofluid-oil relative permeability curves. Results showed that, at low PP variations of 0.1, 2, and 5 MPa, two-phase flow parameters exhibited distinct trends. Thus, for water-oil relative permeability, initial water (S wi ) and residual oil (S or ) saturations both decreased as PP increased. End-point oil K ro (S wi ) and water K rw (S or ) relative permeabilities both increased for water flooding. Similar trends were observed for nanofluid flooding. End-point mobility ratio and displacement efficiency both increased with increase in PP within this range for water and nanofluid flooding. At 10 MPa PP, S wi decreased compared to low PP variations, while S or increased significantly. Similar observation was made for nanofluid flooding except for S or which had moderate increment. End-point mobility ratio increased significantly for water flooding, but had a slight increase for nanofluid flooding compared to low PP variations. Displacement efficiency decreased for both water and nanofluid flooding compared to low PP variations. At the same PP, water-oil and nanofluid-oil relative permeabilities showed similar S wi and K ro (S wi ) but differing S or and K rw (S or ). The findings provide insights into the effect PP variation on relative permeability and would be important in flooding design considerations.