The South African harmony-singing supergroup Ladysmith Black Mambazo has heroism on its mind as it returns on Saturday to the Troy Savings Bank Music Hall (30 Second St.). Onstage and on their new album “Ilembe: Honoring Shaka Zulu,” the group pays tribute to the warrior king who united the Zulu Nation, their own latest chapter as heroes of music.

Since the early 1960s, Lady Smith Black Mambazo has triumphed over adversity again and again.

First, the singers launched an intrepid musical career under the iron grip of apartheid, creating a harmony vocal style of striking distinctive power.

Second, they dealt with sudden success in 1986 when a super-bright spotlight of fame shone on Paul Simon’s “Graceland” album, maintaining their equilibrium and musical vision with rare aplomb.

Third, they managed to maintain a career as international stars even when that spotlight, and Simon, moved on.

Fourth, they have sustained their creativity while dealing with life and death continuity issues. In 1991, Headman Shabalala (brother of leader Joseph) was shot dead, and in 2002, Joseph was injured in another shooting that proved fatal to his wife of 30 years. The attack was engineered by one of his sons, and the four remaining sons sing with Joseph to this day. Over time, Joseph has gradually replaced his brothers in the group with his sons.

Even this astounding tale of triumph over trouble doesn’t hint at how wonderfully well they sing and how entertainingly silly and athletic they are on stage.

Show time for Ladysmith Black Mambazo on Saturday at the Troy Savings Bank Music Hall is 8 p.m. Tickets are $30, $27, and $15 (students). Phone 273-0038 or visit www.troymusichall.org.