Drug administration can occur through various routes, each of which may result in a different process of elimination. This process is often mixed with nonlinear and linear processes. It's important to understand that a single drug can be metabolized into different metabolites through parallel processes.

For instance, consider the metabolism of sodium salicylate. This compound is metabolized into two distinct substances: a glucuronide and a glycine conjugate. The rate of conjugation depends on the available glycine.

Another example is the pharmacokinetic profile of niacin, which is complex due to extensive first-pass metabolism that is dosing-rate specific. Niacin undergoes metabolism through a conjugation step with glycine to form nicotinuric acid and another pathway that forms nicotinamide adenine dinucleotide. Furthermore, niacin is metabolized to at least N-methylnicotinamide and nicotinamide-N-oxide, which are further metabolized to two other compounds. This explains the nonlinear relationship between niacin dose and plasma drug concentrations following multiple doses of niacin extended-release tablets.

In cases where a drug is administered through a constant intravenous infusion and eliminated through nonlinear pharmacokinetics, it follows zero-order input. On the other hand, orally administered drugs are absorbed through first-order absorption and eliminated through nonlinear pharmacokinetics. These processes can be determined by different equations.

Understanding these processes is crucial in pharmacology, as it helps predict how different drugs will behave in the body, influencing dosing strategies and potential drug interactions.