A fundamentally new approach is proposed for describing Z-pinches when the pinch current is governed to a large extent by strong charge separation, which gives rise to a radial electric field in the nonquasineutral core of the pinch. In the central pinch region with a characteristic radius of about r(0) similar to rootJ(0)/en(e)c part of the total pinch current J(0) < J, is carried by the drifting electrons and the remaining current is carried by ions moving at the velocity v(iz) <similar to> c(2eZJ/m(i)c(3)) in the peripheral region with a radial size of c/omega (pi). In the nonquasineutral core of a Z-pinch, the radial ion " temperature " is on the order of ZeJ(0)/c. The time during which the nonquasineutral region exists is limited by Coulomb collisions between the ions oscillating in the radial direction and the electrons. Since the magnetic field is not frozen in the ions, no sausage instability can occur in the nonquasineutral core of the Z-pinch. In the equilibrium state under discussion, the ratio of the radial charge-separation electric field E-0 to the atomic field E-a may be as large as E0Ea similar to 137(2)(a(0)omega (pe)/c)rootJ/J(Ae), where a(0) is the Bohr radius. (C) 2001 MAIK " Nauka/Interperiodica ".