Business Process Modelling Notation (BPMN) is a visual specification language without well-defined concepts for equivalences. This necessitates the establishment of fundamental notions that underpin the equivalences of BPMN processes. The main body of the paper is centered around the principle of substitutibility in which different types of equivalences of BPMN processes are formally described. Additionally, these results provide a basis for defining the behavioural equivalence of BPMN models. Our research investigation contributes to the field of business process management by developing a tight con-nection between BPMN and its associated equivalence notions.