Unforced invasion of wettability-altering aqueous surfactant Solutions into an initially oil-filled oil-wet capillary tube has been observed to take place very slowly, and because this system is an analogue for certain methods of improved oil recovery from naturally fractured oil-wet reservoirs, it is important to identify the rate-controlling processes. We used a model for the process published by Tiberg et al. (Tiberg, F.; Zhmud, B.: Hallstensson, K.; Von Bahr, M. Phys. Chem. Chem. Phlys. 2000, 2, 5189-5196) and modified it for forced imbibitions. We show that when applied pressure differences are not too large invasion rates are controlled at large times by the value of the bulk diffusion coefficient for surfactant in the aqueous phase and at early times by the resistance to transfer of surfactant from the oil-water meniscus onto the walls of the capillary. For realistic values of the bulk diffusion coefficient, invasion rates are indeed slow, as observed. The model also predicts that the oil-water-solid contact angle during unforced displacement is close to pi/2, and so, the displacement occurs in a state of near-neutral wettability with the rate of invasion controlled by the rate of surfactant diffusion rather than a balance between capillary forces and viscous resistance. Under forced conditions, the meniscus moves faster, but the same kinds of dynamical balances between the various processes as were found in the spontaneous case operate. Once the capillary threshold pressure for entry into the initial oil-wet tube is exceeded, the effect of pressure on velocity becomes more significant, there is not sufficient time for the surfactant molecules to transfer in great quantity from the meniscus to the solid surface, and wettability alteration is then no longer important.