We study the initial value problem for Lovelock and Horndeski theories of
gravity. We show that the equations of motion of these theories can be written
in a form that, at weak coupling, is strongly hyperbolic and therefore admits a
well-posed initial value problem. This is achieved by introducing a new class
of "modified harmonic" gauges for general relativity.HSR is supported by STFC Grants PHY-1504541 and
ST/P000681/1
