In this paper we investigate some issues arising from the introduction of multiple temporal granularities in an object-oriented data model. Although issues concerning temporal granularities have been investigated in the context of temporal relational database systems, no comparable amount of work has been done in the context of object-oriented models. Moreover, the main drawback of the existing proposals is the lack of a formal basis -- which we believe is essential to manage the inherent complexity of the object-oriented data model. In this paper, we provide a complete temporal object-oriented type system supporting multiple temporal granularities and we formally define the set of legal values for our type system. We then address issues related to inheritance, type refinement and substitutability.