For people taking Zestril, a cough is a possible side effect (it is a common side effect with all ACE inhibitors). Keep in mind that your healthcare provider cannot know beforehand if you will have a side effect with a medicine that you have never taken. Therefore, if you notice a cough with Zestril, talk to your healthcare provider. If the cough continues, he or she may recommend switching to another ACE inhibitor or another medicine altogether.