Narrative:

G-iv was descending from FL240 to cross zzzzz intersection at 13;000 feet en route to ZZZ. A320 was at FL270; landing ZZZ1; requesting lower [altitude] because of moderate chop. I observed g-iv descending through FL231 to make the zzzzz restriction; then I issued A320 FL240. A320 started a descent. About thirty seconds later; g-iv climbed back to FL234. I advised g-iv that he must continue descent and not climb. G-iv acknowledged my transmission; and about thirty seconds later declared an emergency - right engine flame-out; five souls on board; requested direct to airport. In the same situation I would tell A320 that they would have to vector off course to get lower sooner. If the pilot agreed; I would vector east of the ZZZ1 arrival to avoid the emergency aircraft and get A320 lower as soon as possible.

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Original NASA ASRS Text

Title: En route Controller described a loss of separation event when an inbound aircraft declared an emergency and failed to adhere to descent instructions.

Narrative: G-IV was descending from FL240 to cross ZZZZZ Intersection at 13;000 feet en route to ZZZ. A320 was at FL270; landing ZZZ1; requesting lower [altitude] because of moderate chop. I observed G-IV descending through FL231 to make the ZZZZZ restriction; then I issued A320 FL240. A320 started a descent. About thirty seconds later; G-IV climbed back to FL234. I advised G-IV that he must continue descent and not climb. G-IV acknowledged my transmission; and about thirty seconds later declared an emergency - right engine flame-out; five souls on board; requested direct to airport. In the same situation I would tell A320 that they would have to vector off course to get lower sooner. If the pilot agreed; I would vector east of the ZZZ1 arrival to avoid the emergency aircraft and get A320 lower as soon as possible.

Data retrieved from NASA's ASRS site as of July 2013 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.