  We argue that Lovelock theories of gravity suffer from shock formation,
unlike General Relativity. We consider the propagation of (i) a discontinuity
in curvature, and (ii) weak, high frequency, gravitational waves. Such
disturbances propagate along characteristic hypersurfaces of a "background"
spacetime and their amplitude is governed by a transport equation. In GR the
transport equation is linear. In Lovelock theories, it is nonlinear and its
solutions can blow up, corresponding to the formation of a shock. We show that
this effect is absent in some simple cases e.g. a flat background spacetime,
and demonstrate its presence for a plane wave background. We comment on weak
cosmic censorship, the evolution of shocks, and the nonlinear stability of
Minkowski spacetime, in Lovelock theories.
