Lite info om provflygningarna från BBC:
KLM genomför just nu teknisk undersökning av planet dom var uppe med. KLMs VD var med på planet under testflygningen.
Lufthansa har gjort 10 testflygningar mellan Frankfurt och Munchen.
Air France skall genomföra en testflygning under söndagen.
Det skall även göras testflygningar över England och Italien under söndagen.
Dutch airline KLM said it flew a Boeing 737-800 up to the usual maximum altitude of 13km (8 miles) on Saturday and Germany's Lufthansa said it flew 10 planes to Frankfurt from Munich at altitudes of up to 8km.
KLM chief executive Peter Hartman, who was on board the plane, said there was "nothing unusual" about the flight. "If the technical examination confirms this... we then hope to get permission as soon as possible to partially restart our operations," he added.
The tests were conducted at the request of the European Union to see whether travel disruption could be alleviated. More trials are due to take place later on Sunday in countries including Britain, France and Italy.
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Air France is to conduct a test flight over south-western France later on Sunday.
EDIT: Citerade en bättre artikel