Let d λ( t) be a given nonnegative measure on the real line R , with compact or infinite support, for which all moments μ k= ∫ R t k dλ(t), k=0,1,…, exist and are finite, and μ 0>0. Quadrature formulas of Chakalov–Popoviciu type with multiple nodes ∫ R f(t) dλ(t)= ∑ ν=1 n ∑ i=0 2s ν A i,νf (i)(τ ν)+R(f), where σ= σ n =( s 1, s 2,…, s n ) is a given sequence of nonnegative integers, are considered. A such quadrature formula has maximum degree of exactness d max=2∑ ν=1 n s ν +2 n−1 if and only if ∫ R ∏ ν=1 n (t−τ ν) 2s ν+1 t k dλ(t)=0, k=0,1,…,n−1. The proof of the uniqueness of the extremal nodes τ 1, τ 2,…, τ n was given first by Ghizzetti and Ossicini (Rend. Mat. 6(8) (1975) 1–15). 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 quadratic convergence, for determining the nodes τ ν, ν=1,2,…,n , which are the zeros of the corresponding σ-orthogonal polynomial, is presented. Finally, in order to show a numerical efficiency of the proposed procedure, a few numerical examples are included.