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In 2016, three new realizations of the International Terrestrial Reference System (ITRS), namely, DTRF2014, ITRF2014, and JTRF2014, have been released. In this paper, we evaluate these ITRS realizations for precise orbit determination of ten high and low Earth orbiting geodetic satellites using satellite laser ranging (SLR) observations. We show the reduction of observation residuals and estimated range biases, when using these new ITRS realizations, as compared with the previous ITRS realization for SLR stations—SLRF2008. Thus, the mean SLR root-mean-square (RMS) fits reduce (improve), on average over all satellites tested, by 3%, 3.6%, 8.1%, and 7.7% at 1993.0–2015.0, when using ITRF2014, DTRF2014, and DTRF2014 with non-tidal loading (NTL), and JTRF2014 realizations, respectively. The improvement of the RMS fits is even larger at 2015.0–2017.0: 14% and 15.5% using ITRF2014 and DTRF2014, respectively. For the altimetry satellite Jason-2, we found improvements in the RMS and mean of the sea surface height crossover differences with the new ITRS realizations, as compared with SLRF2008. We show that JTRF2014, after an editing done for SLR stations Conception and Zimmerwald, and DTRF2014 with NTL corrections result in the smallest RMS and absolute mean fits of SLR observations indicating the best performance among the ITRS realizations tested, while using SLRF2008 and ITRF2014 causes a 0.2–0.3 mm/y trend in the mean of SLR fits at 2001.0–2017.0. [ABSTRACT FROM AUTHOR]