Systematic studies of the superdeformed even-even and odd-even nuclei of Zn isotopes were carried out using the Projected Shell Model. Comparisons between experimental observations and theoretical calculations are presented. It was found that various neutron shell filling configurations significantly contribute to the high spin behavior of these nuclei. The connections between the energy band crossing, the J^((2)) bump, and the transition quadrupole moments with a shape evaluation are also discussed. PACS. 21.10.Re - Collective levels.PACS. 21.60.Cs - Shell model.PACS. 23.20.Lv - Gamma transitions and level energies.