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* Sweden a top destination for asylum seekers in Europe

* Newcomers find it hard to get jobs

* Far right makes gains across Nordic region

By Simon Johnson and Johan Sennero

STOCKHOLM, Sep 2 (Reuters) - Sweden may have one of Europe's most generous immigration regimes but there is flip side - one of the poorest records among wealthy industrialised nations of integrating newcomers, especially thousands of refugees, into its labour force.

That failure to provide jobs, a cornerstone to fuller acceptance into society, has helped create an ethnic underclass, straining Sweden's open-mindedness toward foreigners and fuelling the far right - a trend mirrored across the Nordics.

"I didn't come to Sweden for the welfare. I didn't come to Sweden to ask for a hand-out," said Mahad Mohammed Musse, a 27-year-old anaesthesiologist fluent in Arabic, Somali, English and Russian, who has only found temporary work at Stockholm's tax free airport shops since arriving nearly two years ago.

"I ask only to be allowed to live my life with the education that I have," he added.

Born in Saudi Arabia to Somalian parents, Musse arrived in Sweden in January 2014 and got permanent residency two months later. Musse says he applied to 25 hospitals and health centres just to be allowed to observe Swedish doctors at work, but did not receive a single reply.

A 2013 OECD study said the unemployment rate for foreign-born Swedish citizens is nearly three times more than for those native born - the second worst in the OECD after Norway. Denmark and Finland are also near the bottom of the table.

For years, thousands of refugees have headed to the Nordics, enticed by their traditional openness, strong economies, security and welfare.

Sweden gives automatic residency to Syrian refugees and welcomes more asylum seekers per capita than any other nation in Europe, making it one of the destinations of choice for many of the migrants now making their way across the continent.

Most Swedes are proud of a record that stretches back to welcoming refugees from Chile in the 70s and the Iran-Iraq war in the 80s. Today, many immigrant suburbs feature colourful playgrounds and well-tended parks, a far cry from ghettos of cities like Paris.

But there is a creeping sense that once homogenous societies held together by a strong welfare model are fracturing.

INEQUALITY

Some 15 percent of Sweden is foreign born, similar to the United States and around double the EU average. In Sweden, inequality is growing faster than in most other developed nations.

That has helped fuel the far right, whose arguments that jobs, welfare and cherished social stability are threatened have struck a chord.

A deadly attack on a Copenhagen synagogue at an event promoting free speech and a fatal stabbing by an asylum seeker in an IKEA store in Sweden have strengthened feelings among some Scandinavians that immigrants remain outsiders.

A new mosque in Copenhagen has sparked opposition while hundreds of Finns protested recently against the opening of an asylum centre in Nokia's home town.

Anti-immigrant parties are part of governments in Finland and Norway, while in Denmark the Danish People's Party and Sweden's Sweden Democrats vie for first place in polls.

"We have islands where social problems have become concentrated and unemployment, bad school results and other social problems amplify each other," Sweden's Employment Minister Ylva Johansson said.

"That's not an issue related to how many refugees we take in. Rather it's about failures of integration."

Discrimination, red tape, unions and strict labour laws that make it hard to hire cheap workers, combined with difficulties is learning native languages, have all contributed.

Swedes joke they have the best educated taxis drivers in the world. Iraqis with engineering degrees are not uncommon.

Around 81,000 sought asylum in Sweden last year - second only to Germany. That's good news for a country with a falling working-age population, as long as the newcomers can get jobs.

LANGUAGE HURDLE

Refugees from Syria, Afghanistan and Eritrea need housing and education as well as work. Many are badly traumatised. Few speak Swedish - a major hurdle in finding work.

New arrivals get free language lessons, but segregated housing and schools can mean levels of Swedish remain basic.

"It is very hard. I have experience but no qualifications," said Tarek Ozone, a 25-year-old from Damascus who fled to Sweden via Egypt and Libya to Sicily and then via car and train through Europe to Sweden. He was queuing inside a job centre in a Stockholm suburb, trying to find work as a carpenter.

Sweden awoke to problems of a growing underclass in 2013 when riots erupted in Stockholm's mainly immigrant suburbs, with youths burning cars and battling police blamed for the shooting of a Portugese-born man.

The heart of the riots was in Husby, a stone's throw from Sweden's IT hub of Kista. But many youths complained jobs were out of reach.

"For every 10 applications someone with a Swedish-sounding name has to send to get one job interview, a person called Mohammad Ali has to send 20,", said Moa Bursell, researcher at the Institute for Futures Studies.

It is not just about refugees. Roma migrants who have set up makeshift camps outside Stockholm, begging outside IKEA stores and metro entrances, have shocked Swedes.

The Sweden Democrats, who doubled their vote to 13 percent in the 2014 election, get around 20 percent in polls. Leader Jimmie Akesson has warned of "explosions and shootings nearly every day".

The southern cities of Malmo and Gothenburg in particular have been hit by grenade attacks and shootings in recent months, violence that stands out in a country where it is rare.

"Integration is an impossible project, particularly with levels of immigration we have now," Akesson said.

But Musse, the anaesthesiologist, still hopes to find a job in one of the country's hospitals.

"That is the only thing that keeps me getting up every morning," he said. (Additional reporting by Phil O'Connor and Daniel Dickson; Editing by Alistair Scrutton)