The transverse resistive wall instability in the Two-Beam Accelerator (TBA) is investigated analytically and numerically. Without any damping mechanism, we find one to four e-folds in 100 m, depending on the design. It is found that Landau damping, due to energy spread within a beam slice, is not effective, due to rapid synchrotron oscillations in the FEL ponderomotive well. Damping due to an energy sweep along the beam is also considered and it is found that a small variation in energy along the beam, decreasing from head to tail, can significantly reduce growth. We conclude that the resistive wall instability is not a severe design constraint on a TBA
