The hierarchies of the μ-Camassa-Holm,two-component μ-Camassa-Holm and μ-modified Camassa-Holm equations are constructed from bi-Hamiltonian structures of the Korteweg-de Vries equation,the Ito equation and the modified Korteweg-de Vries equation.The key Hamiltonian operator that includes μ is (e)μ-(e)3x,and the inner product used to define the Jacobi identity of the Hamiltonian operators is defined on the unit circle S1.