A theoretical model is presented that explains slow copper-induced oxidation of low-density lipoprotein in the systems free of seeded hydroperoxydes. The model is based on the probabilistic kinetic theory, modified to take into account different radical generation rates by oxidized and reduced forms of the metal ions. It is shown that the initiation and progression of the LDL oxidation can take place in any LDL dispersion by metal-induced oxidation of alpha-tocopherol, one of the constituents of LDL, and formation of slowly reacting alpha-tocopheroxyl radical. Selected values of several adjustable parameters define actual temporal profiles of the quantities defining the oxidation process.