The Danish Girl is still in limited release, but the film is already picking up awards. Both of its stars, Eddie Redmayne and Alicia Vikander, were both nominated for Golden Globes this morning.

While the latest film from The King’s Speech director Tom Hooper missed out on a nomination for Best Picture - Drama, Vikander was nominated for Best Actress in a Drama and Redmayne for Best Actor. Composer Alexandre Desplat was also nominated for Best Score.

The film tells the story of Lili Elbe, a Danish painter who was one of the first people to ever undergo sex-reassignment surgery. Redmayne stars as Elbe and Vikander plays Gera Wegener.

“I am incredibly grateful to the HFPA for having included me in such a brilliant troupe of actors,” Redmayne said in a statement. “I'm equally thrilled that Alicia and Alexandre have been recognised as well. Having the opportunity to help tell Lili and Gerda’s story has been a great privilege for me, and I am hugely grateful for the guidance, generosity and insight given to me by the transgender community.”

Vikander was also nominated for her supporting role in the sci-fi hit Ex Machina.

“I am truly thrilled and grateful to the HFPA for both of these wonderful nominations! To be considered amongst all these brilliant actresses and their outstanding performances is such an honour,” Vikander said. “Working on The Danish Girl and Ex Machina were such gifts in themselves, and for this to happen is all so exciting. Thank you.”

Vikander is in an interesting position, since Focus Features has been campaigning her role in The Danish Girl as a supporting role. But if the Oscars want to nominate her for Ex Machina, she can’t be nominated twice. The Oscars could decide to ignore Focus and nominate her for Best Actress though.

“I’m not involved in that at all,” she told Entertainment Weekly about the conundrum. “And I don’t think you can be. I mean, for me, I hope you hear it in my voice, I’m just overjoyed. I was in the car on the way to the airport and I was just thinking, ‘I can’t get my head around any of this yet.’”

The Golden Globes are on Jan. 10. The Danish Girl will go wide on Christmas Day.