The delayed radiation-induced fluorescence from polyethylene and its alkyl- and fluorine-substituted analogues doped with aromatic luminophores was studied in the time range of 1-1000 ns. Qualitative analysis of the effects of a magnetic field on the fluorescence decay indicated that, in all polyolefins studied, the main portion of the fluorescence observed arose from the recombination of geminate spin-correlated radical ion pairs (RIPs). In the case of polyethylene, this conclusion was supported by observing the effect of an external electric field on the fluorescence decay. It was shown by comparison with the computer simulation of intratrack recombination that the tunneling character of the RIP recombination, which had an asymptotic time dependence of the geminate recombination rate close to t(-1),was typical of most studied polyolefins at temperatures below 273 K in the time range studied. The increase to room temperature and above caused a gradual transition to a regime where the geminate recombination rate was mainly determined by the migration of RIP partners with time dependence close to t(-3/2). The low estimate of the electron transfer distance upon the ion recombination in this regime was about 2 nm. In polyethylenes, exposed to an irradiation of 0.3-0.4 MGy, the role of charge carrier diffusion became hardly noticeable because of the cross-linking of polyethylene chains and the increase in polymer matrix stiffness. Oxygen, dissolved in a polymer doped with aromatic molecules, caused quenching of the recombination luminescence due to electron transfer from the dopant radical anion to the oxygen molecules. At room temperature, typical distances for such electron transfer were estimated to be similar to 1.5 nm.