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 (Qα > 8 MeV) and analyzing the high energy part of the measured α spectrum, the limit N (Sg)/N (W) < 5.5 × 10 −14 atoms/atom at 90% C.L. was obtained (for Sg half-life of 10 9 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 [L. Cardani et al., JINST 7 (2012) P10022]: N (eka-Bi)/N (Bi) < 1.1 × 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.