We investigate the crystal properties of CdTe nanowires overgrown with HgTe. Scanning electron microscopy (SEM) and scanning transmission electron microscopy (STEM) confirm, that the growth results in a high ensemble uniformity and that the individual heterostructures are single-crystalline, respectively. We use highresolution X-ray diffraction (HRXRD) to investigate strain, caused by the small lattice mismatch between the two materials. We find that both CdTe and HgTe show changes in lattice constant compared to the respective bulk lattice constants. The measurements reveal a complex strain pattern with signatures of both uniaxial and shear strains present in the overgrown nanowires.