A comet whose orbit around the Sun has an eccentricity greater than 1.0. Periodic comets may be injected into hyperbolic orbits following passage close to Jupiter, as with Comet Lexell in 1779. Comets on such trajectories are lost to the Solar System. Some comets making their first visit to the inner Solar System from the Oort Cloud may follow hyperbolic trajectories, never to return. The possibility that some hyperbolic comets come from outside the Solar System cannot be excluded.