The paper deals with the nature of ontological structures. The metaphysical assumption of the existence of ontological structures allows explaining both the singularity of things and cohesion between them. The author adheres to the standpoint of structural realism, according to which ontological structures exist independently of our representation ability. He suggests that things are made up from tropes, and that these tropes are connected with each other by a strong cohesion, which goes beyond the relations of compresence. It is confirmed that the cohesion is grounded in ontological necessity, and that adequate understanding of ontological structures thus requires an appeal to the modality 'de re' which cannot be reduced to the modality 'de dicto'. In this way modal ontology plays a central role in the investigation and description of ontological structures.