  We study the Cauchy problem in a special case of non-linear massive gravity:
the two-tensor "f-g" theory. Despite being ghost-free, it has recently been
argued that the theory is inherently problematic due to the existence of
superluminal shock waves. Furthermore it is claimed that acausal characteristic
can arise for any choice of background. In order to further understand the
causal structure of the theory, we carefully perform a detailed analysis of the
characteristic equations and show that the theory does admit a well-posed
Cauchy problem, i.e., there exist hypersurfaces that are not characteristic
hypersurface. Puzzles remain regarding the existence of a superluminal
propagating mode in both the f-g theory, as well as in the full non-linear
massive gravity. That is, our result should not be taken as any indication of
the healthiness of the theory. We also give a detailed review of
Cauchy-Kovalevskaya theorem and its application in the Appendix, which should
be useful for investigating causal structures of other theories of gravity.
