Solid solutions in the AIN─Al2OC and SiC─AlN systems were fabricated by hot‐pressing powder mixtures in graphite dies. X‐ray diffraction showed the samples to be single phases of 2H structure. The samples were annealed between 1600° and 1900°C for up to 1000 h. In the SiC─AlN system, optical microscopy and X‐ray diffraction failed to reveal microstructural or phase changes. However, electron microscopy showed that samples had decomposed. Streaking of diffraction spots occurred along directions orthogonal to {012} planes (∼43° off the c axis), which is approximately the direction along which the elastic energy function is a minimum. The orientation‐dependent Young's modulus was also a minimum along this direction. In AIN─Al2OC, optical microscopy and X‐ray diffraction indicated the occurrence of decomposition. The precipitates were disk‐shaped with [001] orthogonal to the disks. The occurrence of decomposition along the [001] direction suggests that it is the elastically soft direction.