Summary: Let \(d\lambda(t)\) be a given nonnegative measure on the real line \(\mathbb{R}\), with compact or infinite support, for which all moments \(\mu_t= \int_{\mathbb{R}} f(t) d\lambda(t)\), \(k= 0,1,\dots\), exist and are finite, and \(\mu_0> 0\). Quadrature formulas of Chakalov-Popoviciu type [cf. L. Chakalov, Colloq. Math. 5, 69-73 (1958; Zbl 0081.05801); T. Popoviciu, Acad. Republ. Popul. Romîne, Fil. Iasi, Studii Cerc. Sti., Ser. I 6, No. 1/2, 29-57 (1955; Zbl 0068.05003)] with multiple nodes \[ \int_{\mathbb{R}} f(t) d\lambda(t)= \sum^n_{\nu=1} \sum^{2s_\nu}_{i=0} A_{i,\nu}(\tau_\nu)+ R(f), \] where \(\sigma= \sigma_n= (s_1,s_2,\dots, s_n)\) is a given sequence of nonnegative integers, are considered. Such a quadrature formula has maximum degree of exactness \(d_{\max}= 2\sum^n_{\nu=1} s_\nu+ 2n-1\) if and only if \[ \int_{\mathbb{R}} \prod^n_{\nu=1} (t- \tau)^{2s_\nu+ 1} t^kd\lambda(t)= 0,\quad k= 0,1,\dots, n-1. \] The proof of the uniqueness of the extremal nodes \(\tau_1,\tau_2,\dots, \tau_n\) was given first by A. Ghizzetti and A. Ossicini [Rend. Mat., VI. Ser. 8, 1-15 (1975; Zbl 0303.65021)]. Here, an alternative simple proof of the existence and the uniqueness of such quadrature formulas is presented. In a study of the error term \(R(f)\), an influence function is introduced, its relevant properties are investigated, and in certain classes of functions the error estimate is given. A numerically stable iterative procedure, with quadrature convergence, for determining the nodes \(\tau_\nu\), \(\nu= 1,2,\dots, n\), which are the zeros of the corresponding \(\sigma\)-orthogonal polynomial, is presented. Finally, in order to show a numerical efficiency of the proposed procedure, a few numerical examples are included.