has taken Kate Bosworth
to meet his parents.
The 'True Blood' actor was seen out and about in his native Stockholm, Sweden, with the actress at the weekend, meeting up with friends and spending time with his family.
One source at a coffee shop where the couple were relaxing with pals told E! Online: "They looked so happy together. Kate was rubbing Alex's back and looking up at him affectionately. You can definitely tell they're in love.
"It really seems like they're getting serious."
Alexander and Kate have been romantically linked since last September but despite being photographed together several times, have repeatedly denied they are dating.
However, Kate, 27, recently admitted she "adores" the star, though will only admit they are "very good friends".
When asked about their relationship
status, she said: "That's a minefield, man! I'm not stepping into that. I've learned too well from being on that road.
"We are very good friends, He's a wonderful, wonderful man. I adore him."
Alexander has also been tight-lipped about their romance, claiming recently he is single.
When asked if he would date an actress, Alexander, 34, added: "I don't think that matters...There are pros and cons. It's about a connection. I don't really care what they do for a living if the connection is there."