  We obtain global existence results for the Cauchy problem associated to the
Schrodinger-Debye system for a class of data with infinite mass (L2-norm). A
smallness condition on data is assumed. Our results include data such as
singular-homogeneous functions and some types of data blowing up at finitely
many points. We also study the asymptotic stability of the solutions. Our
analysis is performed in the framework of weak-Lp spaces.
