Local authorities advised residents to stay inside their homes and call police if they see anything.
It is unclear what circumstances lead to the bear's death.
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German media reports have suggested the animals' enclosures were damaged in a storm, after a river overflowed and damaged fences.
Vets are said to be on sight as well as police and firefighters.
As it turned out, the cats had never left the sprawling 30-hectare Eifel Zoo in Luenebach, much of which was under water after huge thunderstorms overnight. It is home to some 400 animals, including around 60 exotic and native animals, according to Eifel Zoo's site.
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Friday's escape comes two years after two lions broke out of their cages at a zoo in Leipzig in eastern Germany.
In 2015, an orang-utan was shot dead after escaping from the Duisburg zoo, and a bear escapee from Osnabrueck suffered the same fate in 2017.
In the end, a drone sighted the remaining escapees inside the zoo compound.
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