It is not uncommon to have a persistent cough after a cold or the flu, especially if you had a productive (wet) cough during the illness. This is because the cough helps to clear out any remaining mucus or irritants from the respiratory tract. A persistent cough after a cold or the flu is usually not a cause for concern and will resolve on its own within a few weeks. However, if the cough is accompanied by other concerning symptoms or persists for an extended period of time, it is important to see a doctor.