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It was revealed on Sunday that America's Gay, the fastest man in the world this year, and Jamaica's former world record holder Powell had both tested positive for banned substances.
It is not known which substance Gay took, although that should be confirmed after his B sample is analysed.
Powell, who has run 9.88secs this year but failed to make the Jamaican team for next month's World Championships, was tested at the national trials in June and returned an adverse finding for oxilofrine, a stimulant that boosts fat-burning.
Jamaica's Sherone Simpson, a three-time Olympic medallist, has also tested positive.
And Coe, vice-president of the international athletics federation IAAF and chairman of the British Olympic Association, is determined to ensure the sport clamps down on doping.
"The most important thing for me is that the testing system is working and for the sake of clean athletes it is very important we do not flinch in our efforts," he said.
"This is not a war we can afford to lose, and it is important for any athlete to know that if they want to risk cheating that they are going to get caught.
"Of course we would rather not wake up to the headlines that we have done today but we have taken a tough stance on doping and will continue to do so.
"We would rather have the short-term embarrassment from the sorts of stories we have today rather than a decline in the sport to a position where no one has any trust in the athletes. That's what we are fighting for.
"We are still waiting for the B samples and as vice-president of the IAAF it is very important we go through this process in a proper way to really understand what we are dealing with.
"But the message is getting through and we are not taking our foot off the pedal."
