The registration period for .eu domain names started on December 7 and since than already more than 166,000 applications have been filed.
Germany accounts for about 33 percent of all applications, followed by The Netherlands at 16 percent and France at 13 percent.
British businesses are a bit more sceptic, only a tenth of the applications came from the UK.
"The demand for .eu has been very strong, though it is worrying that British businesses are so far behind their European rivals in protecting their brands online," NetNames business development director Jonathan Robinson said.
"British companies must act quickly to ensure their online brands are protected across Europe. Applications are dealt with in the order they are received, so any delay could cause your brand significant damage if your trademarks and names are registered by another party," he said.