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The dynamical ages of the opposite lobes of selected giant radio sources are estimated using the DYNAGE algorithm of Machalski et al., and compared with their spectral ages estimated and studied by Jamrozy et al. in Paper II. As expected, the DYNAGE fits give slightly different dynamical ages and other model parameters for the opposite lobes modelled  independently  of each other, e.g. the age ratios are found to be between ∼1.1 and ∼1.4. Demanding similar values of the jet power and the radio core density for the same source, we look for a  self‐consistent  solution for the opposite lobes, which results in different density profiles along them. We also show that a departure from the equipartition conditions assumed in the model, justified by X‐ray observations of the lobes of some nearby radio galaxies, and a relevant variation of the magnetic field strengths may provide an equalization of the ages of the lobes. A comparison of the dynamical and spectral ages shows that a ratio of the dynamical age to the spectral age of the lobes of investigated giant radio galaxies is between ∼1 and ∼5, i.e. similar to that found for smaller radio galaxies. To supplement possible causes for this effect already discussed in the literature, such as uncertainty of the assumed parameters of the model, or influence of a possible departure from the energy equipartition assumption, a further two causes are identified and discussed: (i) a difference between the injection spectral indices describing the initial energy distributions of the emitting relativistic particles determined using the DYNAGE algorithm in the dynamical analysis and in the classical spectral‐ageing analysis, and (ii) a different influence of the axial ratio of the lobes in the estimation of the dynamical age and the spectral (synchrotron) age. Arguments are given to suggest that DYNAGE can better take account of radiative effects at lower frequencies than the spectral‐ageing analysis. The DYNAGE algorithm is especially effective for sources at high redshifts, for which an intrinsic spectral curvature is shifted to low frequencies.

A multifrequency study of giant radio sources – III. Dynamical age versus spectral age of the lobes of selected sources