Non-narcotic antitussives are used to treat coughs caused by the common cold, the flu, and other respiratory infections. They work by suppressing the cough reflex in your brain, helping you to stop coughing. Non-narcotic antitussives come in different forms, including oral pills and syrups. Examples include benzonatate (Tessalon Perles) and dextromethorphan (Delsym).