The grammatical relations are one part of traditional grammar that deals with important concepts such as subject, direct object, and indirect object. The main aim of this paper is to give a descriptive account of the term "grammatical relations hierarchy" in the English language depending on the theory of “Relational Grammar” as it demonstrates the relationship between these syntactic categories. Relational grammar predicates the hierarchy of these syntactic phenomena as subject > direct object > indirect object > non-terms. This paper attempts to describe the importance of these concepts and the hierarchy in the occurrence of these arguments in different constructions in order to identify the most privileged syntactic phenomena. This paper is concerned with giving general information about the concept of grammatical relations and the grammatical relations hierarchy. Then it attempts to show whether the word order of the grammatical relations in the English language obeys this hierarchy. Various constructions have been investigated for the purpose of demonstrating the position of these grammatical relations and the syntactic environments they are privileged to occur. The research has concluded that in the majority of the analyzed linear orders, the subject lies at the top of the hierarchy, and is the most privileged syntactic argument in English sentence constructions. However, in certain syntactic transformations like reflexivization and extraction constructions, it loses this privilege and shares it with other syntactic arguments like direct and indirect objects