After two years, Balslev left the Royal Danish Theater and had her international breakthrough as Senta in Harry Kupfer's staging of Wagner's Der fliegende Holländer at the 1978 Bayreuth Festival.
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In 1976, she made her debut at the Royal Danish Theater as Yaroslavna in Prince Igor.
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Balslev has received several awards and honors, including Tagea Brandt Rejselegat (1996) and the Reumert Prize, of which she was the first recipient (1999).