Leading scientists in the United States say the hole in the ozone layer of the Earth's atmosphere above the Antarctic appears to have stopped widening.
The ozone layer blocks the Sun's ultra-violet rays, exposure to which is harmful to humans, animals and plants.
International agreements were reached to end the use of ozone-depleting chemicals called CFCs after the hole was discovered in 1986.
It is hoped the hole may "heal" fully over the next 60 years.
Two of the scientists whose work helped alert the world to the existence of a hole in the ozone layer in the 1980s told a conference in Washington they were hopeful that the ozone layer was recovering.
"I'm very optimistic that we will have a normal ozone layer sometime, not in my lifetime, but perhaps in yours," said Dr David Hofman, who works for the US National Oceanic and Atmospheric Administration (NOAA) as director of the Global Monitoring Division.
Dr Susan Solomon, of the Intergovernmental Panel on Climate Change, said she was also optimistic.
But she added: "There's a lot more to be done from a scientific perspective in terms of what I would call accountability.
"I think it's very important to make sure that we actually measure ozone - not only not getting any worse, but actually starting to improve, to be sure that the actions we have taken internationally have been effective."
The two scientists reaffirmed their findings at a news conference to mark the 20th anniversary of their research first alerting the world to the problems of ozone-depleting CFCs.
The NOAA said the improvement in the ozone layer was caused largely by the phasing out of CFCs (chlorofluorocarbons) from products such as aerosol sprays and refrigerators.
The production of these chemicals was restricted by the Montreal Protocol which became effective in 1987 - and is deemed a success.
However, the chemicals brought in to replace CFCs are themselves not benign, and are thought to contribute heavily to global warming.
Ozone is a molecule that is composed of three oxygen atoms. It is responsible for filtering out harmful ultra-violet radiation (less than 290 nanometres) from the Sun.
The gas is constantly being made and destroyed in the stratosphere, about 30 km (19 miles) above the Earth. In an unpolluted atmosphere, this cycle of production and decomposition is in equilibrium.
But CFCs and the other Montreal-restricted chemicals will rise into the stratosphere where they are broken down by the Sun's rays. Chlorine and bromine atoms released from the man-made products then act as catalysts to decompose ozone.
The thinning that occurs over the Arctic has never matched that in the southern polar region and it is expected to recover sooner, sometime between 2030 and 2040.