ARE things really heating up this fast between Alexander Skarsgård and Kate Bosworth?

The True Blood star took his girlfriend home to Stockholm, Sweden to meet his friends and family on the weekend, and were spotted on Saturday having coffee in Nytorget, a trendy area of Stockholm.

“They looked so happy together,” said a source. “Kate was rubbing Alex’s back and looking up at him affectionately. You can definitely tell they’re in love.”

The couple were also joined by well-known Swedish actor Andreas Wilson, and happily posed for pictures with fans who approached them. They were again spotted at Asögatan Aaarts restaurant on Sunday.

Kate and Alexander first met on the set of their movie Straw Dogs while filming in Louisiana last year.

Do you think they’re the real deal?

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