Airspace in most of Europe has been reopened but many travellers are still stranded as airlines seek to shift a huge backlog after about 95,000 flights were cancelled in the last week.
Germany's air-traffic controllers said they were gradually reopening the country's airspace on Wednesday, a day after Britain, France and Belgium all allowed at least partial resumption of services.
"There is a good chance that the airspace above Germany and all international airports will remain available until late in the evening," the government agency Deutsche Flugsicherung said.
Denmark said it was to reopen all its airspace from 9:00 GMT on Wednesday.
The Eurocontrol air traffic agency in Brussels predicted that the number of take-offs and landings in Europe would be close to normal by Friday.
Volcano ash chaos
An ash cloud from a volcano eruption on Iceland caused air traffic authorities across Europe to close airspace over most of the continent and millions of people were affected.
The Eyjafjallajoekull volcano has been spewing ash and lava for days, but since the weekend, the eruption has lost nearly 80 per cent of its intensity, a spokeswoman for Iceland's civil protection agency said on Wednesday.
The airport shutdowns have cost the airline industry $200 million a day, according to the International Air Transport Association (IATA).
Giovanni Bisignani, the IATA chief, told Italian television that more than five medium- and small-sized European airlines risked bankruptcy in the fall-out from the ash cloud shutdowns and called for EU compensation.
At London's Heathrow, Europe's busiest airport, the first flight landed on Tuesday night after a five-day shutdown.
Al Jazeera's Imran Khan, reporting from Heathrow, said: "Planes are coming in every couple of minutes and, obviously, it is a very joyous sight for a lot of those stranded travellers.
"When people were watching the arrivals board and saw the sign that said 'landed', there were screams of excitement."
With more than 95,000 flights cancelled across the world, it will be some time before the airlines are able to clear the backlog of passengers.
British Airways, which cancelled about 500 flights a day in the past five days, said it was trying to clear its backlog on a case-by-case basis.
It said travellers could either rebook online or claim a full refund, and it also urged travellers booked to fly this week to consider cancelling their trips so that it could maximise space to fly people home.
Spain's Iberia said it was coping with the backlog by using bigger aircraft and adding extra flights.
"We've never had a backlog like this before," Laurie Price, the director of aviation strategy at consultant Mott Macdonald, said.
"After 9/11 airspace was shut for three days, and then the US airlines were bailed out by the government."