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We study the behavior of r-fold zeta-functions of Euler-Zagier type with identical arguments ζ_r(s,s,…,s) on the real line. Our basic tool is an “infinite” version of Newton's classical identities. We carry out numerical computations, and draw graphs of ζ_r(s,s,…,s) for real s, for several small values of r. Those graphs suggest various properties of ζ_r(s,s,…,s), some of which we prove rigorously. When s∈[0,1], we show that ζ_r(s,s,…,s) has r asymptotes at ℜs=1/k (1≤k≤r), and determine the asymptotic behavior of ζ_r(s,s,…,s) close to those asymptotes. Numerical computations establish the existence of several real zeros for 2≤r≤10 (in which only the case r=2 was previously known). Based on those computations, we raise a conjecture on the number of zeros for general r, and gives a formula for calculating the number of zeros. We also consider the behavior of ζ_r(s,s,…,s) outside the interval [0,1]. We prove asymptotic formulas for ζ_r(−k,−k,…,−k), where k takes odd positive integer values and tends to +∞. Moreover, on the number of real zeros of ζ_r(s,s,…,s), we prove that there are exactly (r−1) real zeros on the interval (−2n,−2(n−1)) for any n≥2. © 2021 Elsevier Inc.