  We consider the superposition of the first two members of the gravitational
hierarchy (Einstein plus first Gauss-Bonnet(GB)) interacting with the
superposition of the first two members of the $SO_{(\pm)}(d)$ Yang--Mills
hierarchy, in $d$ dimensions. Such systems can occur in the low energy
effective action of string theory. Particle-like solutions %for the systems
with only an Einstein term, and with only a GB term, in dimensions $d=6,8$ are
constructed respectively. Our results reveal qualitatively new properties
featuring double-valued solutions with critical behaviour. In this preliminary
study, we have restricted ourselves to one-node solutions.
