The effectiveness of foam for mobility control in the presence of oil is key to foam enhanced oil recovery (EOR). A fundamental property of foam EOR is the existence of two steady-state flow regimes: the high-quality regime and the low-quality regime. Experimental studies have sought to understand the effect of oil on foam through its effect on these two regimes. Here, we explore the effect of oil on the two flow regimes for one widely used foam model. The STARS (CMG 2015) foam model includes two algorithms for the effect of oil on foam: In the “wet-foam” model, oil changes the mobility of full-strength foam in the low-quality regime, and in the “dry-out” model, oil alters the limiting water saturation around which foam collapses. We examine their effects as represented in each model on the two flow regimes using a Corey relative permeability function for oil. Specifically, we plot the pressure-gradient contours that define the two flow regimes as a function of superficial velocities of water, gas, and oil, and show how oil shifts behavior in the regimes. The wet-foam model shifts behavior in the low-quality regime with no direct effect on the high-quality regime. The dry-out model shifts behavior in the high-quality regime but not the low-quality regime. At fixed superficial velocities, both models predict multiple steady states at some injection conditions. We perform a stability analysis of these states using a simple 1D simulator with and without incorporating capillary diffusion. The steady state attained after injection depends on the initial state. In some cases, it appears that the steady state at the intermediate pressure gradient is inherently unstable, as represented in the model. In some cases, the introduction of capillary diffusion is required to attain a uniform steady state in the medium. The existence of multiple steady states, with the intermediate one being unstable, is reminiscent of catastrophe theory and of studies of foam generation without oil. @en