The Camassa–Holm hierarchy can be regarded as isospectral flows of the inhomogeneous string. In this talk, I will introduce a nonisospectral extension of the second flow in the Camassa–Holm hierarchy (GN2ndCH) together with its multipeakons based on classical determinant technique. It is shown that a reduction of the peakon dynamical system of the GN2ndCH equation results in the generalized nonisospectral 2mCH interlacing peakon dynamical system. Moreover, a special case of the proposed equation is investigated and a new phenomenon of 2-peakon is observed.