Bradley, Renée Get Cozy in Barcelona

Bradley, Renée Get Cozy in Barcelona
Bradley Cooper and Renée Zellweger on Aug. 11
KADENA PIX/Bauer Griffin

08/12/2009 AT 01:10 PM EDT

Sure, they're both in the upcoming Code 39, but Renée Zellweger and Bradley Cooper have been more than cozy costars in Barcelona this week.

The funnyman was in town to premiere his hit comedy The Hangover, but Cooper, 34, and Zellweger, 40, also clocked plenty of private time together. The two were first spotted at JFK airport hopping a flight to Spain. Later, they were photographed at the luxury Hotel Arts Barcelona – Cooper with his arm around Zellweger while she tucked her hand into his back pocket. They were also photographed having breakfast together and doing some sightseeing at a local church.

Bradley, Renée Get Cozy in Barcelona| Couples, Bradley Cooper, Renee Zellweger

At a church in Barcelona

KADENA PIX / Bauer Griffin

Earlier this summer, the duo was spotted dining in the Upper East Side, and before the trip to Spain, Zellweger paid a visit to the Smyth Hotel, where Cooper was staying.

"They tried to keep the visits very low-key," a source said at the time.

So, what's the story between the two? "It's very new," a source says. "It's just the beginning."

But a pal of Zellweger's is rooting for the romance. "They make a great couple," the friend says. "He's a gentleman and she's so sweet. They get along well; they have fun together, and they're really happy."

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