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In this present paper the authors deploy a novel technique,a method based on using quasi-optical dielectric resonator (QDR), to measure reactance properties of HTS films at millimeter (mm) frequencies. The technique has been shown earlier to use for accurate measurements of the film surface resistance Rs. However a challenge to analogous measurement of HTS surface reactance still remains. The latter is connected with a number of difficulties which must be overcome in order to obtain Xs from the measurement results as follows: 1) necessity of temperature dependence knowledge of material dielectric constant ε which the given resonator is made of; 2) some nonreproducibility of eigen frequencies for the QDR with conducting endplates (CEP) at rearrangements of the resonator; 3) absence of rigid electrodynamic analysis of open ODR and impossibility, in this connection, of finding eigen frequencies for the QDR with perfect CEP.