Energy resolution, alpha/beta ratio, and the pulse shape discrimination ability of the ZnWO_4 crystal scintillators were studied. The radioactive contamination of a ZnWO_4 crystal was investigated in the Solotvina Underground Laboratory. Possibilities to apply ZnWO_4 crystals for the dark matter and double beta decay searches are discussed. New improved half-life limits on double beta decay in zinc isotopes were established, in particular, for ECbeta^+ decay of 64-Zn as: T_1/2^2nu > 8.9 10^18 yr and T_1/2^0nu > 3.6 10^18 yr, both at 68% CL.
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