  We present an extension of the methods of classical Lie group analysis of
differential equations to equations involving generalized functions (in
particular: distributions). A suitable framework for such a generalization is
provided by Colombeau's theory of algebras of generalized functions. We show
that under some mild conditions on the differential equations, symmetries of
classical solutions remain symmetries for generalized solutions. Moreover, we
introduce a generalization of the infinitesimal methods of group analysis that
allows to compute symmetries of linear and nonlinear differential equations
containing generalized function terms. Thereby, the group generators and group
actions may be given by generalized functions themselves.
