She replayed Raymonda in 2003 and the same year appeared in Esmeralda which was performed at the Notre Dame de Paris and was produced by Roland Petit.
Her breakthrough performance was in 1964 with Les Biches, and she performed in narrative ballets like Swan Lake and Raymonda.
The NNBT has performed at the Kennedy Center in Washington, D.C. (Asami Maki's Raymonda in February 2008), and will also perform Asami Maki's version of La dame aux camellias, as a guest company at the Bolshoi Theatre in September 2009.
She, along with Andris Liepa, was the first Soviet dancer to appear as a guest performer with the New York City Ballet in 1988 (she had danced in "Raymonda Variations", "Apollo" and "Symphony in C" there).