[en] In order to determine the suitability of using a superconducting radio frequency (SRF) linac to generate XUV radiation, the beam dynamics in such a linac have been simulated using a vectorized two dimensional beam breakup code, TDBBU. The energy spread and emittance of the accelerated beam are determined as a function of current for a linac like CEBAF and for a linac optimized for high peak currents. The results indicate that there are significant improvements in transverse emittance growth possible by going to lower RF frequencies and by utilizing BNS phasing in the accelerating cavities. In the first section of this paper the simulation is described. Next, the transverse and longitudinal wakes typical in superconducting cavities are discussed. The results of the simulations are given, followed by a comparison of a linac driven FEL and a typical storage ring driven FEL. The conclusion of the work is that the former scheme looks promising because higher average power is possible. 4 refs., 6 figs., 3 tabs