  We construct a Ramsey class whose objects are Steiner systems. In contrast to
the situation with general $r$-uniform hypergraphs, it turns out that simply
putting linear orders on their sets of vertices is not enough for this purpose:
one also has to strengthen the notion of subobjects used from "induced
subsystems" to something we call "strongly induced subsystems".
  Moreover we study the Ramsey properties of other classes of Steiner systems
obtained from this class by either forgetting the order or by working with the
usual notion of subsystems. This leads to a perhaps surprising induced Ramsey
theorem in which designs get coloured.
