Room temperature ionic liquids (IL) find increasing use for the replacement of organic solvents in practical applications, including their use in solar cells and electrolytes for metal deposition, and as extraction solvents for the reprocessing of spent nuclear fuel. The radiation stability of ILs is an important concern for some of these applications, as previous studies suggested extensive fragmentation of the constituent ions upon irradiation. In the present study, electron paramagnetic resonance (EPR) spectroscopy has been used to identify fragmentation pathways for constituent anions in ammonium, phosphonium, and imidazolium ILs. Many of these detrimental reactions are initiated by radiation-induced redox processes involving these anions. Scission of the oxidized anions is the main fragmentation pathway for the majority of the practically important anions; (internal) proton transfer involving the aliphatic arms of these anions is a competing reaction. For perfluorinated anions, fluoride loss following dissociative electron attachment to the anion can be even more prominent than this oxidative fragmentation. Bond scission in the anion was also observed for NO3- and B(CN)(4)(-) anions and indirectly implicated for BF4- and PF6- anions. Among small anions, CF3SO3- and N(CN)(2)(-) are the most stable. Among larger anions, the derivatives of benzoate and imide anions were found to be relatively stable. This stability is due to suppression of the oxidative fragmentation. For benzoates, this is a consequence of the extensive sharing of unpaired electron density by the pi-system in the corresponding neutral radical; for the imides, this stability could be the consequence of N-N sigma(2)sigma(-1) bond formation involving the parent anion. While fragmentation does not occur for these "exceptional" anions, H atom addition and electron attachment are prominent. Among the typically used constituent anions, aliphatic carboxylates were found to be the least resistant to oxidative fragmentation, followed by (di)alkyl phosphates and alkanesulfonates. The discussion of the radiation stability of ILs is continued in the second part of this study, which examines the fate of organic cations in such liquids.