A search for the double beta decay of zinc and tungsten isotopes has been performed with the help of radiopure ZnWO4 crystal scintillators (0.1-0.7 kg) at the Gran Sasso National Laboratories of the INFN. The total exposure of the low background measurements is 0.529 kg yr. New improved half-life limits on the double beta decay modes of 64Zn, 70Zn, 180W, and 186W have been established at the level of 10^{18}-10^{21} yr. In particular, limits on double electron capture and electron capture with positron emission in 64Zn have been set: T_{1/2}(2 u 2K) > 1.1 10^{19} yr, T_{1/2} (0 u 2epsilon) > 3.2 10^{20} yr, T_{1/2} (2 u epsilon beta^+) > 9.4 10^{20} yr, and T_{1/2} (0 u epsilon beta^+) > 8.5 10^{20} yr, all at 90% C.L. Resonant neutrinoless double electron capture in 180W has been restricted on the level of T_{1/2} (0 u 2epsilon) > 1.3 10^{18} yr. A new half-life limit on alpha transition of 183W to the metastable excited level 1/2^- 375 keV of 179Hf has been established: T_{1/2} > 6.7 10^{20} yr.
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