Abstract. We consider query execution strategies for object-oriented distributed databases. There are several scenarios of query decomposition, assuming that the corresponding query language is fully compositional, i.e. allows decomposing queries into subqueries addressing local servers. Compositionality is a hard issue for known OO query languages such as OQL. Thus we use the Stack-Based Approach (SBA) and its query language SBQL, which is fully compositional and adequate for distributed query optimization. We show flexible methods based on decomposition of SBQL queries in a distributed environments. Decomposition can be static or dynamic, depending on the structure of the query and distribution of data. The paper presents only the main assumptions, which are now the subject of our study and implementation.