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The rigidity dependence of all Forbush decreases (FDs) recorded from 1995 to 2015 has been determined using neutron monitor (NM) and Solar and Heliospheric Observatory (SOHO) (EPHIN) spacecraft data, covering the energy (rigidity) range from ∼433 MeV (1 GV) to 9.10 GeV (10 GV). We analyzed a total of 421 events and determined the spectrum in rigidity with an inverse power-law fit. As a result, the mean spectral index was identified to be 〈γF〉 = 0.46 ± 0.02. The majority (∼66%) of the FDs have γF within the range 0.3–0.7. The remaining one-third of the events (∼33%) have either (very) soft or hard FD spectra, with the latter being more common than the former. Significant variations of γF occur within almost every FD event. During the initial FD decay phase the spectrum becomes gradually harder, in contrast to the recovery phase, when it becomes softer. Additionally, low energies (rigidities) seem to be better suited for studying the fine structure of interplanetary disturbances (primarily interplanetary coronal mass ejections) that lead to FDs. In particular, FDs recorded by the EPHIN instrument on SOHO better capture a two-step structure than FDs observed by NMs. Finally, the ejecta of an ICME, especially when identified as a magnetic cloud, often leads to abrupt changes in the slope of γF. [ABSTRACT FROM AUTHOR]