  We present a simple class of mechanical models where a canonical degree of
freedom interacts with another one with a negative kinetic term, i.e. with a
ghost. We prove analytically that the classical motion of the system is
completely stable for all initial conditions, notwithstanding that the
conserved Hamiltonian is unbounded from below and above. This is fully
supported by numerical computations. Systems with negative kinetic terms often
appear in modern cosmology, quantum gravity and high energy physics and are
usually deemed as unstable. Our result demonstrates that for mechanical systems
this common lore can be too naive and that living with ghosts can be stable.
