Most of the inter-parliamentary institutions are part of an intergovernmental organization.
Such branches of intergovernmental organizations are typically established in order to provide for representation of citizens, rather than governments who are represented in other bodies within the organization.
Most of the inter-parliamentary institutions do not hold legislative power and have a consulting or informal cooperation-stimulating role.
[1] When the intergovernmental organization chooses to operate through a hybrid system of not only intergovernmentalism, but also supranationalism an organization-level legislature is established (or a predecessor inter-parliamentary institution is granted legislative power) in the form of international parliament.
Members of international parliaments could be assigned in the same way as members of inter-parliamentary institutions or in cases of more advanced supranationalism they could be directly elected.