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We obtain explicit and simple conditions which in many cases allow onedecide, whether or not a Denjoy domain endowed with the Poincare orquasihyperbolic metric is Gromov hyperbolic. The criteria are based on theEuclidean size of the complement. As a corollary, the main theorem allows todeduce the non-hyperbolicity of any periodic Denjoy domain.

Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics