What is always in a oxidation- reduction reaction?

I believe oxygen and hydrogen are always included in a redox reaction. I am basing this conclusion on the fact that, whether these reactions are occurring in a basic solution (add OH- and H20 to balance) or an acidic solution (add H+ and H2O to balance), you use both oxygen and hydrogen in the chemical equation.
Extra info about these fascinating reactions:
After assigning oxidation numbers to the given chemical equation, extract the ones who's oxidation numbers change from the reactants to the products (there should only be two that change). Put these into separate equations with the reactant and its oxidation number and the product and its oxidation for both elements. Then, to equalized the oxidation numbers, add electrons on the appropriate side.
Remember:
Electrons can only be added, but since they have a negative charge, it is like subtracting them. Add electrons to the most positive side of each elements equation. The number of electrons added to either element must be equivalent. To make them so, find the smallest number they both can be divided into (LCD). Multiply each (whole equation) by the number required to make them the LCD.
After which, you can place the new coefficients you found and place them back into the original equation. Then, using conventional methods, you can balance the equation. All element can be balanced this way except for hydrogen and oxygen. Add the appropriate elements (given above), depending on the type of solution, to balance.
Important:
Oxidation is the loss of electrons, when electrons are added to the product. The oxidized element is the ironically referred to as the reducing agent.
Reduction is the gain of electrons, when electrons are added to the reactants. The reduced element is, in turn, referred to as the oxidizing agent.