Trace amounts of copper ion catalyst induce exotic phenomena in the oxidation of several inorganic sulfur compounds by peroxides in aqueous solution. Simple and complex oscillations and several kinds of bistability are observed when the copper(II)-catalyzed oxidation of S2O32- by either H2O2 or S2O82- is carried out in a CSTR and when SCN- ions are oxidized with H2O2 in the presence of copper ions under either batch or flow conditions. For the S2O32--H2O2-Cu(II) reaction, a four-step model is proposed, in which formation of the intermediate HOS2O3- and attack on that species by S2O32- and H2O2 play key roles. When this core of reactions is extended with additional steps, computer simulations yield good agreement between the experimentally observed and calculated pH oscillations, bistability and batch behavior. In the oscillatory S2O32--S2O82--Cu(II) flow reaction, Cu(I), Cu(II) and Cu(III) species as well as SO4.- and S28O3.-, are postulated to participate in a free radical mechanism, which successfully simulates the oscillations. To model the experimentally observed oscillations and bistability in the H2O2-SCN--Cu(II) system, we have proposed a complex mechanism involving 30 reactions and 26 independent species.