Modelling cultural heritage is a research topic shared by a broad scientific community.  Although  this subject has been widely studied, it  seems that  some  aspects  still  have  to  be  tackled.  This paper describes two CIDOC (ICOM’s International Committee for Documentation) Conceptual Reference Model (CRM) extension proposals (A & B) dedicated to structuring knowledge concerning historical objects and historical events.  It  focuses  on  multiple  interpretations and sequential reality, this last being a concept which does not exist in CIDOC CRM but was originally developed in another conceptual model, the Multiple Interpretation Data Model (MIDM). To begin, an extensive description of MIDM concepts is given as well as a recall of its main peculiarities. It is followed by a mapping proposed to translate MIDM concepts into ontologies  devoted to describing cultural  heritage  entities  and  activities,  the CIDOC CRM  and  compatible  models. Unfortunately,  some MIDM  concepts  are  not  covered  by this  mapping  because  they  do  not  match  with existing  CRM entities and properties, and this paper explains why an extension is necessary. It describes how the two versions of the extension proposal cover the missing MIDM concepts. One of these two versions, the proposal A, has been implemented as ontology in Protégé and has been tested through an instantiation phase using a real example. This instantiation phase is fully detailed. It shows that proposal A works coherently with CRM ontologies. On another hand, instantiation phase highlights improvements needs such as recording chronology in a structured way. Highlights: • Cultural Heritage modelling involves two different ontological concepts: reality and information held about it. • Historical Objects existence is a sequence made by events, stability periods and changes affecting it. • Multiple Interpretation Data Model mapping to CIDOC CRM and its extension proposal take into account difference between reality and information. They also manage sequence concept.