In weakly coupled, current biased, doped semiconductor superlattices. domai
n walls may move upstream against the flow of electrons. For appropriate do
ping values, a domain wall separating two electric-field domains moves down
stream below a first critical current, it remains stationary between this v
alue and a second critical current, and then moves upstream above. These co
nclusions are reached by using a comparison principle to analyze a discrete
drift-diffusion model, and validated by numerical simulations. Possible ex
perimental realizations are suggested.