A technique of analyzing the isotopic composition of Lu and Hf and for determining the Lu/Hf and Hf/Hf isotopic ratios in zircons is presented using a Neptune Plus (Thermo Scientific) mass spectrometer with inductively coupled plasma with an NWR 213 (ESI) laser ablation attachment. On the example of Mud Tank, GJ-1, 91500, Plesovice and Temora-2 standard zircon samples, the uncertainty of a single measurement of the 176Hf/177Hf ratio has been obtained in the range of 0.002-0.008% in the form of 2σ (with a crater diameter of 50 μm; when it decreased to 25 μm the measurement uncertainty of the 176Hf/177Hf ratio increased by 1.5-2 times). Under the optimum parameters of the NexION 300S with NWR213 with the aim of increasing the locality of the sequential study of U/Pb and Lu/Hf isotope systems, a comparative characteristic of the application of two approaches has been obtained: in adjacent grain areas (approach 1) and in one crater (approach 2). The metrological characteristics of analyzing the isotopic composition of Lu and Hf and for determining the Lu/Hf and Hf/Hf isotopic ratios in zircons have been determined. To establish the application limits of the developed technique, the factor planning of the experiment has been developed. It was established that with a Lu/Hf ratio of 1/50 or more, the technique is not recommended to be applied due to the incorrect allowance of the isobaric effect. The procedures for measuring and calculating the Lu/Hf isotopic ratios of the isotope system in zircon have been tested on zircon grains (samples NP-46 and NP-47) of the Neplyuevsky pluton (South Urals). The data obtained was in satisfactory agreement with the data of the A. P. Karpinsky Russian Geological Research Institute (VSEGEI).