This paper is extracted from the dissertation "Reflocutionary (Non)speech Acts in Arthur Miller's Death of a Salesman and Salah Abd El-Sabour's Ma'sat Al-Hallaj (The Tragedy of Al-Hallaj): A Cognitive Pragmatic Study".The paper aims at investigating a fourth dimension to Austin's classification of speech acts into locutionary, illocutionary, and perlocutionary acts; that is reflocutionary acts. It tackles this act from a cognitive pragmatic paper, in order to manifest the psychological and mental processes needed to carry out such an act appropriately. Moreover, this paper applies reflocutionary both speech and non-speech acts to Arthur Miller's Death of a Salesman which is rich of psychological and cognitive aspects among its characters, that makes it applicable to reflocutionary acts. Being appropriate for this study, the descriptive and analytical methods will be followed to apply reflocutionary acts to the selected play. The current study has concluded that reflocutionary acts represent the effect or reflection of illocutionary acts on the speaker himself/herself. Moreover, reflocutionaries are performed either by speech or non-speech acts. Reflocutionary (non)speech acts included retractions, telling lies, responding according the partner's need, criticizing, confessing, selfrealizing, self-criticizing, regretting, expressing jealousy, censuring, self-blaming, pitying, sympathizing, compensating, encouraging, praising, admiring, justifying, and other acts in the selected play.