  This paper analyses two-player nonzero-sum games of optimal stopping on a
class of linear regular diffusions with not non-singular boundary behaviour (in
the sense of It\^o and McKean (1974), p.\ 108). We provide sufficient
conditions under which Nash equilibria are realised by each player stopping the
diffusion at one of the two boundary points of an interval. The boundaries of
this interval solve a system of algebraic equations. We also provide conditions
sufficient for the uniqueness of the equilibrium in this class.
