X-ray computed tomography (CT) is regarded by many as the third revolution in coordinate metrology. This may be explained by the holistic approach of CT, which scans workpieces completely and allows a great variety of measurements. With a single scan, it is possible to make for example, dimensional, form or wall thickness measurements, or even to compare the entire workpiece with e.g. its nominal geometry, and more. The same holistic approach also greatly facilitates the quality control of multi-material (MuMat) objects, even in their assembled state. However, the lack of international standards describing specifications and technical guidelines for the application of CT as a coordinate measurement system (CMS) hinders the trust in this X-ray-based technology. As yet, no published international standard for CT as a CMS exists, but such a standard is already under development in the international standardisation committee ISO TC213 WG10 "coordinate measuring machines". This underdevelopment standard will only cover monomaterial measurements, although the demand for a systematic and traceable approach for evaluating the performance of CT systems while measuring multi-material workpieces is growing. Therefore, this thesis has as its primary objective the development of an acceptance test to evaluate the performance of CT-based CMSs for multi-material measurements. Existing principles and concepts from the ISO 10360 series of international standards were applied or adapted to the proposed multi-material test. New test principles and concepts, considering the specifics of multi-material measurements with CT, were developed as well. A widely accepted concept for the evaluation of the system performance (based on the ISO 10360) is the assessment of the probing error (P) and length measurement error (E). These systems characteristics are assessed based on test measurements carried out with appropriate reference standards. Thus, to evaluate the multi-material performance of CT systems based on P- and Etests, and to verify the developed proposal, novel multi-material spheres and hole cube standards were designed, manufactured, calibrated and measured with CT at the PhysikalischTechnische Bundesanstalt (PTB). In addition, CT simulations were carried out as well. In total twelve standards featuring different multi-material combinations were created and tested during this thesis. Several experimental investigations for different multi-material parameters were carried out on the developed multi-material standards. The results evidenced the multi-material influence on both P- and E-test measurements. The proposed multi-material acceptance test proved to be a suitable approach for the performance verification of CT-based CMS for multi-material measurements.