  We review the notion of reducibility and we introduce and discuss the notion
of orbital reducibility for autonomous ordinary differential equations of first
order. The relation between (orbital) reducibility and (orbital) symmetry is
investigated and employed to construct (orbitally) reducible systems. By
standard identifications, the notions extend to non-autonomous ODEs of first
and higher order. Moreover we thus obtain a generalization of the lambda
symmetries of Muriel and Romero. Several examples are given.
