  An analysis of wavefront motion in weakly coupled doped semiconductor
superlattices is presented. If a dimensionless doping is sufficiently large,
the superlattice behaves as a discrete system presenting front propagation
failure and the wavefronts can be described near the threshold currents $J_i$
($i=1,2$) at which they depin and move. The wavefront velocity scales with
current as $|J-J_i|^{{1\over 2}}$. If the dimensionless doping is low enough,
the superlattice behaves as a continuum system and wavefronts are essentially
shock waves whose velocity obeys an equal area rule.
