  We contribute to the classification of toroidal circle planes and flat
Minkowski planes possessing three-dimensional connected groups of
automorphisms. When such a group is an almost simple Lie group, we show that it
is isomorphic to $\text{PSL}(2,\mathbb{R})$. Using this result, we describe a
framework for the full classification based on the action of the group on the
point set.
