For part of his recital Sunday at the Kennedy Center, legendary flutist Sir James Galway performed with local students. (Paul Cox)

Sir James Galway’s last visit to Washington, in 2013, was billed as a legacy tour. The Irish flutist, a legend by any measure, was still at the top of his game, and he had the audience eating out of his hand.

On Sunday afternoon, Galway was back, presented again by Washington Performing Arts in the Kennedy Center Concert Hall, and playing a platinum Nagahara flute he helped design. But this time around, the less-than-full house and increasing shortcomings in finger agility and tuning gave the impression of an artistic arc beginning its descent.

At 76, Galway still worked marvels in many pieces, not least in the outrageous variations of Giulio Briccialdi’s “Carnival of Venice,” where the complex writing gives the impression of the flute accompanying its own melody. Galway has certainly not lost the sense of how to spin out a beautiful phrase, heard in the meandering, Gallic-cool third sonata by Philippe Gaubert. His breath support flagged at crucial moments for some of the very high notes, which just wilted, as in Cécile Chaminade’s “Concertino,” and intonation woes reached a nadir in the “Serenade” from Riccardo Drigo’s “Les Millions d’Arlequin.”

His wife, flutist Jeanne Galway, joined in for Franz and Karl Doppler’s “Rigoletto Fantasy,” although not in as pristine form as when they played it in 2013, and Phillip Moll provided steady, patient backup on the piano. An endless succession of encores seemed to outlast the audience’s enthusiasm, including when eight flute students performed with the Galways for one of Joseph Bodein de Boismortier’s concertos for five flutes. The entire Columbia Flute Choir, from Falls Church, Va., made Henry Mancini’s “Pie in the Face Polka” sound like something from a crazy calliope before Galway finally brought the program to a close, with his beloved flute-and-piano version of “Danny Boy.” It was, he said, his way of “blessing the house.”