  We study nonlinear dynamics in models of Lorentz-violating massive gravity.
The Boulware-Deser instability restricts severely the class of acceptable
theories. We identify a model that is stable. It exhibits the following bizarre
but interesting property: there are only two massive propagating degrees of
freedom in the spectrum, and yet long-range instantaneous interactions are
present in the theory. We discuss this property on a simpler example of a
photon with a Lorentz-violating mass term where the issues of (a)causality are
easier to understand. Depending on the values of the mass parameter these
models can either be excluded, or become phenomenologically interesting. We
discuss a similar example with more degrees of freedom, as well as a model
without the long-range instantaneous interactions.
