  We discuss the concept of gauge-invariant fields for non-abelian gauge
theories. Infinitesimal fluctuations around a given gauge field can be split
into physical and gauge fluctuations. Starting from some reference field the
gauge-invariant fields are constructed by consecutively adding physical
fluctuations. An arbitrary gauge field can be mapped to an associated gauge
invariant field. An effective action that depends on gauge-invariant fields
becomes a gauge-invariant functional of arbitrary gauge fields by associating
to every gauge field the corresponding gauge-invariant field. The
gauge-invariant effective action can be obtained from an implicit functional
integral with a suitable "physical gauge fixing". We generalize this concept to
the gauge-invariant effective average action or flowing action, which involves
an infrared cutoff. It obeys a gauge-invariant functional flow equation. We
demonstrate the use of this flow equation by a simple computation of the
running gauge coupling and propagator in pure $SU(N)$-Yang-Mills theory.
