We present a new method to measure the shear elastic moduli and viscosities of erythrocyte membranes which is based on the fixation and transient deformation of cells in a high-frequency electric field. A frequency domain of constant force (arising by Maxwell Wagner polarization) is selected to minimize dissipative effects. The electric force is thus calculated by electrostatic principles by considering the cell as a conducting body in a dielectric fluid and neglecting membrane polarization effects. The elongation A of the cells perpendicular to their rotational axis exhibits a linear regime (A proportional to Maxwell tension or to square of the electric field E2) at small, and a nonlinear regime (A proportional to square root of Maxwell tension or to the electric field E) at large extensions with a cross-over at A approximately 0.5 micron. The nonlinearity leads to amplitude-dependent response times and to differences of the viscoelastic response and relaxation functions. The cells exhibit pronounced yet completely reversible tip formations at large extensions. Absolute values of the shear elastic modulus, mu, and membrane viscosity, eta, are determined by assuming that field-induced stretching of the biconcave cell may be approximately described in terms of a sphere to ellipsoid deformation. The (nonlinear) elongation-vs.-force relationship calculated by the elastic theory of shells agress well with the experimentally observed curves and the values of mu = 6.1 x 10(-6) N/m and eta = 3.4 x 10(-7) Ns/m are in good agreement with the micropipette results of Evans and co-workers. The effect of physical, biochemical, and disease-induced structural changes on the viscoelastic parameters is studied. The variability of mu and eta of a cell population of a healthy donor is +/- 45%, which is mainly due to differences in the cell age. The average mu value of cells of different healthy donors scatters by +/- 18%. Osmotic deflation of the cells leads to a fivefold increase of mu and 10-fold increase of eta at 500 mosm. The shear modulus mu increases with temperature showing that the cytoskeleton does not behave as a network of entropy elastic springs. Elliptic cells of patients suffering from elliptocytosis of the Leach phenotype exhibit a threefold larger value of mu than normal discocytes of control donors. Cross-linking of the spectrin by the divalent S-H agents diamide (1 mM, 15 min incubation) leads to an eightfold increase of mu whereas eta is essentially constant. The effect of diamide is reversed after treatment with S-S bond splitting agents.