  Just recently, the class of all Einstein-Maxwell fields solving
simultaneously also any higher-order modification of the Eintein-Maxwell theory
has been completely identified. In the present work, we argue that, in view of
our recent results on nonabelian gauge fields, analogous identification can be
in fact achieved for Einstein-Yang-Mills fields associated with any compact and
semisimple gauge group. In particular, any such solution consists of a $VSI$
(vanishing scalar invariant) spacetime metric and a $VSI$ gauge field, both
subject to a simple tensorial condition. Based on that, we are able to provide
explicit form of all such solutions and interpret them as gravitational and
Yang-Mills plane-fronted waves propagating in flat spacetime along the common
recurrent wave vector. The results have consequences also for theories with a
richer field content, which is further illustrated on 10D heterotic
supergravity.
