Molecular dynamics simulations were performed for compressed C-60, C-180 and C-60@C-180 fullerene molecules, and the semi-empirical PM3 calculations were carried out to obtain the electronic structure of the compressed fullerenes. According to the obtained results, the differences of mechanical properties between these compressed fullerenes, as well as the changes of their FMO (Frontier molecular orbital) energy-levels during compression, were discussed. It is shown that (1) the C-60 molecule has much higher load-support and energy-absorbing capability than the C-180 and C-60@C-180 molecules, and the C-60@C-180 is only slightly superior to the C-180, (2) of the three molecules, the C-60 molecule has the best chemical-stability, and the C-60@C-180 molecule has the worst one, (3) with the increase of compressive strain, both the C-60 and C-60@C-180 molecules become more chemically active, and (4) when the compressed C-180 molecule caves in at the loading position(s), its chemical-stability decreases abruptly.