Raman spectra of onion-like carbon nanospheres (OCNSs) have been studied under pressure up to 48 GPa. A transformation related to a change from sp(2) to sp(3) bonding of carbons in OCNSs was observed at pressures above 20 GPa. The Raman spectra exhibit some vibrational features similar to those of the theoretically proposed Z-carbon phase of cold-compressed graphite, while the transition pressure is obviously higher than that for graphite. In contrast to the transformations in compressed graphite, interlayer bonds are formed on the nanoscale between buckled layers in OCNSs under pressure due to the concentric configuration, and sp(2)-sp(3) conversion is incomplete even up to 48 GPa. This is confirmed by TEM observations on the decompressed samples. Moreover, the onion-like carbon structure is extremely stable and can be recovered even after a compression cycle to 48 GPa. This high stability, beyond that of other sp(2) carbon materials, is related to the unique onion-like configuration and to the interlayer bonding. The transformed material should have excellent mechanical properties so that it can sustain very high pressure.