The O-O bond breaking reactions of peroxynitrous acid and methyl peroxynitrite, ROONO (R = H, Me), were investigated theoretically using the (U)CCSD/6-31+G*, (U)CCSD(T)/6-31+G*//(U)CCSD/6-31+G*, and CBS-QB3 methods. The OONO dihedral angle has a remarkably large influence on the barriers for cleavage of the O-O bonds, which influences the subsequent radical recombination to yield nitrates (RONO2). A barrier of ca. 18-19 kcal/mol is predicted for RO-ONO dissociation involving a (2)A(1)-like NO2 fragment in transition states beginning from a cis-OONO conformation. This pathway is significantly favored relative to a B-2(2)-like transition state with a trans-ONOO conformation; the latter has a barrier of 33-34 kcal/mol. Notably, the favored cis-OONO pathway is "electronically correct" (because (2)A(1) NO2 is a N-centered radical), but "geometrically incorrect" for subsequent N-O bond formation to yield RONO2. The imperfect initial orientation of RO/NO2 for N-O bond formation rationalizes some escape of free radicals, in competition with low-barrier RO. and NO2 orientational motions followed by near-barrierless collapse to RONO2. For HOONO, the pathway for HONO2 formation may include a hydrogen-bonded intermediate, .(OHONO)-O-...., earlier proposed as a source of one-electron processes occurring after O-O bond cleavage. The cis-ONOO rearrangement barrier is in accord with the experimental free energy of activation (18 +/- 1 kcal/mol) for the rearrangement of peroxynitrous acid (HOONO) into nitric acid (HNO3) MeOONO has a similar rearrangement mechanism, although the pathways for its rearrangement lack any hydrogen-bonded intermediates.