  A scenario for the generation of the baryon asymmetry in the early Universe
is proposed in which cosmic string loops, predicted by theories where the
baryon and/or lepton numbers are gauged symmetries, collapse during the
friction dominated period of string evolution. This provides a mechanism for
the departure from thermal equilibrium necessary to have a nonvanishing baryon
asymmetry. Examples of models are given where this idea can be implemented. In
particular, the model with the gauge symmetry $SU(3)_{c}\otimes
SU(2)_{L}\otimes U(1)_{Y}\otimes U(1)_{B} \otimes U(1)_{L}$ has the interesting
feature where sphaleron processes do not violate the baryon and lepton numbers
so that no wash out of any initial baryon asymmetry occurs at the electroweak
scale.
