The cross section for ZZ --> ZZ with arbitrarily polarized Z bosons is calculated within the electroweak standard model including the complete O(alpha) corrections. We show the numerical importance of the radiative corrections and elaborate its characteristic features. The treatment of the Higgs-boson resonance is discussed in different schemes including the S-matrix-motivated pole scheme and the background-field method. The numerical accuracy of the equivalence theorem is investigated by comparing the cross sections for purely longitudinal Z bosons obtained from the equivalence theorem and from the complete calculation. In this context the full O(alpha) corrections are also confronted with the enhanced corrections of O(alpha M-H(2)/s(w)(2)M(w)(2)), which were frequently used in the literature.