It is difficult to exchange parametric assembly models using conventional neutral formats such as the standard for the exchange of product model data or the initial graphics exchange specification. These formats only support the boundary representation information that leads to the inability to perform parametric re-evaluation, once a model is exchanged. In order to exchange parametric information along with the design intent, a design history-based macro-parametric approach was proposed. Our method is macro-parametrics approach, however, supported only the exchange of individual part models. As most of the products are manufactured in assemblies, where several components are connected with multiple constraints, it is necessary to exchange the assembly model data. To overcome the issue of post-exchange editability, a collection of neutral assembly commands was introduced to extend the capabilities of the macro-parametric approach. A set of neutral assembly constraints was defined and a system for exchanging the parametric assembly models was implemented. An assembly model consisting of coaxial and incidence constraints was successfully exchanged between two commercial computer-aided design systems: CATIA and NX. It was possible to re-evaluate the assembly model parametrically after the exchange. The method can be further extended to exchange the remaining constraint types in different commercial computer-aided design systems.