Inorganic fullerene-like (IF) nanoparticles made of metal dichalcogenides have previously been recognized to be good friction modifiers and anti-wear additives under boundary lubrication conditions. The tribological performance of these particles appears to be a result of their size, structure and morphology, along with the test conditions. However, the very small scale of the IF nanoparticles makes distinguishing the properties which affect the lubrication mechanism exceedingly difficult. In this work, a high resolution transmission electron microscope equipped with a nanoindentation holder is used to manipulate individual hollow IF-WS(2) nanoparticles and to investigate their responses to compression. Additional atomistic molecular dynamics (MD) simulations of similarly structured, individual hollow IF-MoS(2) nanoparticles are performed for compression studies between molybdenum surfaces on their major and minor axis diameters. MD simulations of these structures allows for characterization of the influence of structural orientation on the mechanical behavior and nano-sheet exfoliation of hollow-core IF nanoparticles. The experimental and theoretical results for these similar nanoparticles are qualitatively compared.