To improve performance of object-oriented database processing, integration between parallel and object-oriented technologies is sought. In this paper, we concentrate on path expression queries. Parallelization of path expression queries can be achieved through simultaneous processing among objects (inter-object parallelization), or concurrent processing among classes (inter-class parallelization). These two parallelization models view parallel object-oriented query processing from two different angles, particularly from an object point of view and from a class point of view, respectively. We also present performance measurements through an implementation which highlight the strengths and the weaknesses of each parallelization model.