The complex pattern of thermal maturity in lower Paleozoic strata of the Arctic Archipelago is thought to have resulted from three events: burial by Mid to Upper Devonian strata over much of the Arctic islands, burial in the northern part of the islands by strata of the Sverdrup Basin, and Jurassic-Cretaceous rifting in the western Arctic. Key risks for hydrocarbon generation in lower Paleozoic strata are that: 1) hydrocarbon generation occurred before structural traps developed over much of the islands; and 2) there is an increased chance of petroleum destruction and/or leakage during the long time since hydrocarbon generation (380 m.y.). Preservation may be possible where evaporites acted as a seal, or where hydrocarbon generation took place more recently. Two conceptual hydrocarbon plays are envisaged: 1) On eastern Bathurst Island, Lower Ordovician carbonates and overlying evaporites were folded during the Early Devonian. Hydrocarbons generated from Silurian source rock intervals during Late Devonian burial on western Bathurst Island could have migrated into these pre-existing fold traps and been preserved by the salt seal; 2) Devonian strata were thin on northeastern Melville Island, Cameron Island, and below the Sverdrup Basin to the north, and Silurian source units retained most of their hydrocarbon-generating potential at the end of the Ellesmerian Orogeny. Burial by sediments of the Sverdrup Basin may have been sufficient to drive Silurian source units back into the oil or gas windows. Hydrocarbons generated during this second burial phase could be held in traps within the lower Paleozoic or the upper Paleozoic and Mesozoic successions. On Banks Island, Jurassic-Cretaceous rifting is inferred to have produced the high level of thermal maturity. However, little is known of the pre-Jurassic thermal history or source rocks.