Unsaturated dialdehydes and their epoxides are toxic products involved in aerosol formation and in the chemistry of the photochemical smog. They are detected when benzene is oxidatively degradated in the troposphere or in experiments that simulate tropospheric conditions. This theoretical study is focused at assessing the viability of some benzene oxidation channels that lead to their formation and could either follow or flank the previously studied pathway to hexa-2,4-diene-1,6-dial (muconaldehyde). In the former case, further oxidative degradation of muconaldehyde entails NO intervention and easily leads to glyoxal and butenedial, as secondary oxidation products. In the latter case, the pathways examined branch from an early intermediate in benzene oxidation, the 2-hydroxy-cyclohexadienyl peroxyl radical, and originate either from the corresponding oxyl radical VI (the "channel VI") or from the bicyclic endo-peroxy allyl-radical intermediate XIII, generated by the closure of a peroxy bridge (the "channel XIII"). The channel XIII can produce epoxy muconaldehyde without NO involvement, as well as some epoxy butenedial, glyoxal, and butenedial, as minor products and through NO-mediated pathways. Though the epoxy aldehydes could also form from the radical VI, through NO-mediated pathways, this is not competitive with the formation of muconaldehyde from VI. How a variable NO concentration can modulate the relative importance of the channel XIII vs the channel VI is estimated. Other pathways have been investigated and discarded as less favorable.