  We study a class of normal affine surfaces with additive group actions which
contains in particular the Danielewski surfaces in $\ba^{3}$ given by the
equations $x^{n}z=P(y)$, where $P$ is a nonconstant polynomial with simple
roots. We call them Danielewski-Fieseler Surfaces. We reinterpret a
construction of Fieseler \cite{Fie94} to show that these surfaces appear as the
total spaces of certain torsors under a line bundle over a curve with an
$r$-fold point. We classify Danielewski-Fieseler surfaces through labelled
rooted trees attached to such a surface in a canonical way. Finally, we
characterize those surfaces which have a trivial Makar-Limanov invariant in
terms of the associated trees.
