[en] The data collected with a radioactively pure ZnWO₄ crystal scintillator (699 g) in low background measurements during 2130 h at the underground (3600 m w.e.) Laboratori Nazionali del Gran Sasso (INFN, Italy) were used to set a limit on possible concentration of superheavy eka-W (seaborgium Sg, Z = 106) in the crystal. Assuming that one of the daughters in a chain of decays of the initial Sg nucleus decays with emission of high energy α particle ($Q_{\mathrm{\alpha <!--\; ??\; -->}}><!--\; >\; -->8$ MeV) and analyzing the high energy part of the measured α spectrum, the limit N(Sg)/N(W) $<<!--\; <\; -->5.5\times <!--\; ??\; -->{10}^{-<!--\; ???\; -->14}$ atoms/atom at 90% C.L. was obtained (for Sg half-life of 10⁹ yr). In addition, a limit on the concentration of eka-Bi was set by analysing the data collected with a large BGO scintillation bolometer in an experiment performed by another group (Cardani et al 2012 JINST 7 P10022): N(eka-Bi)/N(Bi) $<<!--\; <\; -->1.1\times <!--\; ??\; -->{10}^{-<!--\; ???\; -->13}$ atoms/atom with 90% C.L. Both the limits are comparable with those obtained in recent experiments which instead look for spontaneous fission of superheavy elements or use the accelerator mass spectrometry. (paper)