The self-fields generated by the propagation of pulsed electron beams through the wiggler fields in free-electron lasers are calculated and shown to be diamagnetic. A one-dimensional theory for pulsed beams is applied to proposed designs for fourth generation light sources of high-intensity X-rays, which employ beams with current densities of several hundred MA/cm(2). The theory indicates that the diamagnetic effect is unlikely to affect either the growth length or the fundamental emission energy and bandwidth of these devices. (C) 1999 Elsevier Science B.V. All rights reserved.