We study dilaton electrodynamics in Bat spacetime and exhibit a set of
global cosmic-string-like solutions in which the magnetic flux is con
fined. These solutions continue to exist for a small enough dilaton ma
ss but cease to exist above a critical value depending on the magnetic
flux. There also exist domain wall and Dirac monopole solutions. We d
iscuss a mechanism whereby magnetic monopoles might have been confined
by dilaton cosmic strings during an epoch in the early universe durin
g which the dilaton was massless.