Prime Minister Theresa May's Brexit speech is being seen in Europe as the "hard" option of full UK withdrawal - and there is some relief that the British position is clearer now.
"Finally we have a little more clarity re the British plans," German Foreign Minister Frank-Walter Steinmeier said.
Germany also wanted a "close and trusting relationship", he said.
The Czech Europe Minister, Tomas Prouza, tweeted: "UK's plan seems a bit ambitious".
"Trade as free as possible, full control on immigration... where is the give for all the take?" he asked.
The Italian daily La Repubblica commented: "Out of the EU, out of common market, out of everything. It appears that Theresa May's intention through negotiations with the EU at the end of March is 'a hard Brexit' - a very hard Brexit indeed."
One of the top EU officials, European Council president Donald Tusk, voiced regret but some relief too in a tweet: "Sad process, surrealistic times but at least more realistic announcement on #Brexit."
Belgian liberal Guy Verhofstadt, named as the European Parliament's lead negotiator on Brexit, warned that any deal for the UK would be worse than EU membership.
He said it was an "illusion" for Mrs May to suggest "that you can go out of the single market, that you can go out of the customs union and that you can cherry-pick, that you can have still a number of advantages - I think that will not happen".
Mrs May's mention of a possible alternative economic model for the UK was a "threat", he said, that could obstruct the negotiations.
Norway model rejected
Norway's Aftenposten daily said Mrs May's speech signalled "a clear rejection of a Norwegian-type involvement in the [EU] internal market".
Norway has very close ties to the EU - as a member of the European Economic Area (EEA) it has open, tariff-free access to the EU single market, though Norwegian fisheries and agriculture are excluded.
The price for that advantage is high Norwegian contributions to the EU budget and automatic acceptance of most EU laws.
"Even though she rejects the term, it is indeed a hard Brexit," commented France's Le Figaro daily.
Marine Le Pen's far-right National Front (FN) in France praised Mrs May's speech.
FN vice-president Florian Philippot tweeted: "Bravo to T. May who respects her people with a 'clear and clean' Brexit. Sovereignty cannot be a half-measure. French independence soon!"
'The full whack'
Michael Fuchs, a close conservative ally of German Chancellor Angela Merkel, accused Mrs May of "cherry-picking" in her speech, Sky News reported in a tweet.
EU politicians have stressed that they will not let the UK "cherry-pick" parts of its EU membership terms.
They insist that the single market's four freedoms - covering goods, services, capital and labour - cannot be diluted.
The Dutch daily Algemeen Dagblad called Mrs May's speech "not just a bit of Brexit but the full whack".
"Bye bye EU... the unspoken, big threat from London is creating a tax paradise in front of the gates of Europe," it said.
Sweden's former Foreign Minister Carl Bildt tweeted: "I regret the approach the UK government has taken.
"I think most of the EU would have preferred a closer relationship with the UK."
Sweden has long been one of the UK's closest allies in the EU.