2000–2002: Commercial peak

From April to June 2000, Hamasaki released the "Trilogy", a series of singles consisting of "Vogue", "Far Away", and "Seasons". The lyrics of these songs focused on hopelessness, a reflection of Hamasaki's disappointment that she had not expressed herself thoroughly in any of her previous lyrics and a sense of shame of her public image. Likewise, many of the songs she wrote for her subsequent studio album, Duty (September 2000), involved feelings of loneliness, chaos, confusion, and the burden of her responsibilities.
Duty resonated with fans: the "Trilogy" were "hit singles" ("Seasons" was a million-seller); the album itself became Hamasaki's best-selling studio album. At the end of 2000, Hamasaki held her first New Year countdown concert at the Yoyogi National Gymnasium.
In 2001, Avex forced Hamasaki to release her first compilation album, A Best, on March 28.
I am... (January 2002) marked several milestones for Hamasaki. The lead single, "M", was the first of the many tracks from the album that she composed herself, under the pseudonym "Crea". In 2002, Hamasaki held her first concert outside Japan, at the MTV Asia music awards ceremony in Singapore. she received the award for "Most Influential Japanese Singer in Asia". In support of I am..., Hamasaki held two tours, Ayumi Hamasaki Arena Tour 2002 A and Ayumi Hamasaki Stadium Tour 2002 A; the latter was her first tour held in outdoor venues. In November 2002, as "Ayu", she released her first European single, "Connected", a trance song from I am... composed by DJ Ferry Corsten. It was released in Germany on the Drizzly label.
Realizing that English was a "common global language", she used it for the first time on her next studio album, Rainbow (December 2002). The album had three singles—"Free & Easy", "Voyage", and "H"; the last became the best-selling single of 2002.