Several feedback loops are required in the Beam Delivery System (BDS) of the International Linear Collider (ILC) to preserve the luminosity in the presence of dynamic imperfections. Realistic simulations have been carried out to study the performance of the beam-beam deflection based fast feedback system, for both e+e− and e−e− modes of operation. The beam-beam effects in the e−e− collisions make both the luminosity and the deflections more sensitive to offsets at the interaction point (IP) than in the case of the e+e− collisions. This reduces the performance of the feedback system in comparison to the standard e+e− collisions, and may require a different beam parameter optimization.