The nth degree b-equation is read as  with  and positive integer n.  Let ξ = x − ct, where constant c > 0 is called wave speed. When n = 1, it is well-known that the equation has peakon u = ce −|ξ| but no antipeakon. In this paper, we show that when n ≥ 2, the equation has both of peakon and antipeakon, and is the bifurcation wave speed of these two types of waves.