Unsaturated radicals, containing different number of delocalized electrons, are formed via H-atom abstractions with CH(3), iso-C(3)H(7), OOH and OH radicals from (Z,Z) and (E,E)-hepta-2,5-dienes. These reactions and the relative stability of the different allyl-type radicals formed, were studied within the BH&HLYP method, using a 6-311+G(3df,2p) basis set, as well as within the G3MP2 level of theory on BH&HLYP/6-31G(d) geometries. The biallyl type radicals (involving 5 electrons delocalized on 5 carbon atoms) are more stable, by about 47.6 +/- 0.4 kJ mol(-1), than monoallyl type radicals (which involve 3 electrons delocalized on 3 carbon atoms). Three types of the H-atom abstractions were distinguished: direct H-abstraction with CH(3), indirect abstraction with a higher barrier height with iso-C(3)H(7), OOH and a non-direct quasi-barrierless H-abstraction with OH radicals. These observations were also confirmed by the activation entropy versus activation enthalpy as well as the Evans-Polányi's plots. The OOH-hepta-2,5-diene complexes are found to be extremely stable (from -19.6 to 22.3 kJ mol(-1)). The room temperature rate constants were calculated with transition state theory. Formations of monoallyl and biallyl radicals through H-abstraction with OH are fast; the calculated rate constants range from 5.84 x 10(-11) to 1.92 x 10(-9) cm(3) molecule(-1) s(-1) at room temperature. These reactions may play a key role in the "very low temperature combustion" like biological oxidations.