Europe wants to be a USA with it's EU. But the problem with Europe is that is has too much history and tradition, thus refuse to imagine a European with 50% nonwhites. Thus they tend to limit immigration, they even have "immigrant districts" in some of their countries.
Wow, some of you yankees have bizzarre ideas of what it's like over here!
The EU has no united immigration policy. EU members have an open borders policy, which means as an EU citizen I can move to any EU country whenever I like. There's even whole communities of migrant workers who move around following the seasonal work and similar (quite a lot from the newer East European member states).
For immigrants from outside of the EU it's still handled at a national level, although there are EU guidelines (and there is a push for a united EU common policy, but I can't see that coming to fruition while nationalists still hold a large influence in national governments). Immigration problems are dependent on the country. Over here in the UK legal migrants aren't a problem, it's Asylum seekers which are the main issue (both those making valid claims and those making fraudulent claims).
Immigration also depends on the country, not all immigrants are non-white. Here in Britain we see plenty of white immigrants (Recent events in Zimbabwe for example saw a large exodus of the white population to here). There are also sizeable populations of Russians, Slavs, South Africans and Australian ex-pats. Spain and Portugal sees the majority of it's immigrants come from South America, most of whom are of Spanish descent. In fact, the main 'coloured' migrants are to Britain (usually from former African or Carribean colonies, mainly Commonwealth countries), France (North African, though again sizeable numbers are of French descent originally) and Holland (North Africans again).
In fact, black migration to Britain at least has been dropping since the fifties, while Eastern European migration is rising. Most of the black population currently living in Britain are second or third generation British citizens.
It's not the black immigrants who cause the problem either, it's the governments. Germany wants to dictate economic policy, which none of the other members are happy with, many members complain about the voting agreement between Germany and France while Britain can't decide if it wants to be a full member or not. In addition, you also get the squabbles which have been going on for a few hundred years (Cypress refusing to accept Turkey's membership for example).