  The exact operator solutions of two-dimensional anomaly-free chiral abelian
gauge theories are obtained. We show that anomaly-cancellation conditions arise
as consistency requirements of these solutions. For a certain class of flavour
symmetries, fermion condensates are constructed. These are shown to violate the
fermion-number conservation rule. The models are extended to include massive
fermions. We propose a bosonised lagrangian for the massive theory and verify
that it complies with the Gupta-Bleuler condition.
