  Actions of Lie groups on presymplectic manifolds are analyzed, introducing
the suitable comomentum and momentum maps. The subsequent theory of reduction
of presymplectic dynamical systems with symmetry is studied. In this way, we
give a method of reduction which enables us to remove gauge symmetries as well
as non-gauge ``rigid'' symmetries at once. This method is compared with other
step-by-step reduction procedures. As particular examples in this framework, we
discuss the reduction of time-dependent dynamical systems with symmetry, the
reduction of a mechanical model of field theories with gauge and non-gauge
symmetries, and the gauge reduction of the system made of a conformal particle.
