Little information exists on the movements of Gyrfalcons Falco rusticolus outside the breeding season, particularly amongst High Arctic populations, with almost all current knowledge based on Low Arctic populations. This study is the first to provide data on summer and winter ranges and migration distances. We highlight a behaviour previously unknown in Gyrfalcons, in which birds winter on sea ice far from land. During 2000–2004, data were collected from 48 Gyrfalcons tagged with satellite transmitters in three parts of Greenland: Thule (northwest), Kangerlussuaq (central-west) and Scoresbysund (central-east). Breeding home-range size for seven adult females varied from 140 to 1197 km2 and was 489 and 503 km2 for two adult males. Complete outward migrations from breeding to wintering areas were recorded for three individuals: an adult male which travelled 3137 km over a 38-day period (83 km/day) from northern Ellesmere Island to southern Greenland, an adult female which travelled 4234 km from Thule to southern Greenland (via eastern Canada) over an 83-day period (51 km/day), and an adult female which travelled 391 km from Kangerlussuaq to southern Greenland over a 13-day period (30 km/day). Significant differences were found in winter home-range size between Falcons tagged on the west coast (383–6657 km2) and east coast (26 810–63 647 km2). Several Falcons had no obvious winter home-ranges and travelled continually during the non-breeding period, at times spending up to 40 consecutive days at sea, presumably resting on icebergs and feeding on seabirds. During the winter, one juvenile female travelled over 4548 km over an approximately 200-day period, spending over half that time over the ocean between Greenland and Iceland. These are some of the largest winter home-ranges ever documented in raptors and provide the first documentation of the long-term use of pelagic habitats by any falcon. In general, return migrations were faster than outward ones. This study highlights the importance of sea ice and fjord regions in southwest Greenland as winter habitat for Gyrfalcons, and provides the first detailed insights into the complex and highly variable movement patterns of the species.