The coarsening process in a class of driven systems exhibiting striped stru
ctures is studied. The dynamics is governed by the motion of the driven int
erfaces between the stripes. When two interfaces meet they coalesce thus gi
ving rise to a coarsening process in which l(t), the average width of a str
ipe, grows with time. This is a generalization of the reaction-diffusion pr
ocess A + A --> A to the case of extended coalescing objects, namely, the i
nterfaces. Scaling arguments which relate the coarsening process to the evo
lution of a single driven interface are given, yielding growth laws for l(t
), for both short and long times. We introduce a simple microscopic model f
or this process. Numerical simulations of the model confirm the scaling pic
ture and growth laws. The results are compared to the case where the stripe
s are not driven and different growth laws arise.