Using the time domain analysis we studied the processes of oscillation
s build-up and spatial synchronization in FEL's with two-dimensional d
istributed feedback driven by a large size sheet and tubular relativis
tic electron beams. It is proved that proposed feedback mechanism allo
ws to ensure powerful spatial-coherent radiation when the ratio betwee
n transverse size of the electron beam and wavelength runs up to 10(2)
-10(3).