Since the mammals were introduced by man hundreds of thousands of seabirds have been driven away from one of the most important breeding grounds in the tropical Atlantic.
Three biologists met on the British island this weekend to investigate the size of the rat and cat population, how they might be eliminated and how much the various options might cost.
The rats arrived on ships hundreds of years ago and the cats were brought in to control them in 1815. Both prospered.
Seabirds' eggs and nestlings are eaten by the rats while the cats kill the parents, and also dig out the hatchlings of green turtles which swim 1,300 miles from Brazil to lay and bury their eggs.
Only one bird species, the sooty tern, now breeds on the main island and about 20,000 of these fall prey to cats each year.
The masked, red-footed and brown boobies, the brown and black noddies and the unique Ascension frigate bird are found only on inaccessible cliffs or on offshore rocks.
''This is the most important island for seabirds in the tropical Atlantic, but its potential is woefully unfulfilled,'' said Jim Stevenson, who runs the investigation from the Royal Society for the Protection of Birds' Bedfordshire headquarters.
The front-running option is to put out poisoned bait around the coastline, possibly using British military helicopters, but first the team will have to find whether this would harm other wildlife.
Later in the year Mr Stevenson will fly out to try to convince the locals there is a case for eliminating the cats and rats. All pet cats will have to be neutered, and no fertile cats ever allowed in.
Mr Stevenson said: ''You can't have an education programme based solely on killing cats. We will have to convince the key players in the community and the schoolchildren of their island's value to seabirds.''
The £30,000 expedition, led by New Zealand wildlife consultant Brian Bell, is being mainly funded by the British government, with the RSPB and the World Wide Fund for Nature each providing £5,000.Reuse content