for generations; from generation to generation — continued across multiple generations.
私の家は代々農家を営んできた。
My family has run a farm for generations.
この寺は代々この地域の人々に信仰されてきた。
This temple has been venerated by people in the area for generations.
その家系は代々医者を輩出している。
That family has produced doctors for generations.