Julio Medem wrote the part of Alba for Elena Anaya. When the actress accepted the role, she and Medem went to Russia to cast the perfect Dasha. After seeing a lot of actresses and models, they found the perfect one, but the night before this woman was to fly to Spain to start rehearsals, her husband read the screenplay and forbade her to play the role which involved nudity and lesbian lovemaking scenes. However, after returning from Russia dejected, Medem and Anaya found Russian-born model Natasha Yarovenko while casting in Spain, specifically in Barcelona, who accepted the role.
When Alba tells Dasha that her two-wheeled vehicle is called the "Aspasia," Dasha smiles and says she knows after whom it was named. Aspasia was the lover (and maybe wife) of Pericles, the leader during Athen's Golden Age in the Fifth Century B.C. when the arts flourished and the Parthenon was built.
The voice of Sasha, Natasha's (real name Dasha) twin sister is actually voiced by the same actress Natasha Yarovenko which was recorded during post production.
The song sung by Natasha/Dasha and Alba in the shower is "Nel Blu Dipinto Di Blu," commonly known as "Volare" in the U.S. It was a worldwide hit (including number one in the U.S.) for Domenico Modugno in 1958. The lyrics describe a dream that the singer knows will never happen again in which he is painted blue and flying ("volare") and singing ("cantare") in the sky. A non-literal English translation of the song was a hit by Bobby Rydell in the U.S. in 1960.
Five different languages are spoken in the movie; English, Spanish, Russian, Italian, and Basque. English is the primarily language spoken by the two lead characters, Elena and Natasha, to each other. Elena talks to herself in her native Spanish, and Natasha talks to herself in her native Russian. Natasha speaks fluent Italian (to the hotel staff). Except for Basque (one line is spoken by Elena), Natasha is shown to speak fluent English, Russian, and Italian and seems to understand Spanish while Elena is speaking it to her on occasion (despite that Natasha doesn't have a single phrase of Spanish in the movie), but it never becomes clear whether Natasha can speak Spanish too.