Lovelock theories are the most general diffeomorphism invariant theories of gravity in higher dimensions with second order equations of motion. Horndeski theories are the most general diffeomorphism invariant theories of gravity coupled to a scalar field in four dimensions with second order equations of motion. In this talk I will discuss well-posedness of the initial value problem for these theories. Previous work has shown that (generalised) harmonic gauge does not give a well-posed initial value problem. I will describe recent work with Aron Kovacs in which we introdued a modification of harmonic gauge that does give a well-posed initial value problem provided that the theory remains “weakly coupled”. Our modified harmonic gauge may also have applications in conventional GR.