The excellent shock-absorbing performance of WS2 and MoS2 nanoparticles with inorganic fullerene-like structures (IFs) under very high shock wave pressures of 25 GPa is described. The combined techniques of X-ray diffraction, Raman spectroscopy, X-ray photoelectron spectroscopy, thermal analysis, and transmission electron microscopy have been used to evaluate the diverse, intriguing features of shock recovered IFs, of interest for their tribological applications, thereby allowing improved understanding of their antishock behavior and structure-property relationships. Two possible failure mechanisms are proposed and discussed. The supershock-absorbing ability of the IF-WS2 enables them to survive pressures up to 25 GPa accompanied with concurrent temperatures of up to 1000 degrees C without any significant structural degradation or phase change making them probably the strongest cage molecules now known.