In this work we develop a theory of reduced electric linear dichroism transients of DNA fragments in aqueous solution. The DNA fragments are modelled as rigid 'bent-rod molecules' (BRM) with the following physical parameters: electric charge, electric polarizability tensors and hydrodynamical ones, and the average transition probability tensor per molecule. In order to study the growth and decay of electric dichroism transients, the orientational distribution function of the molecules is needed. This function is obtained by solving the time-dependent Fokker-Planck equation in the presence of a low electric field E, using a perturbation method and the Fourier method with time-dependent coefficients. In our calculations the origin of the coordinate system is the mass centre of the BRM. With respect to this centre, the electric dipole moment of the molecule is zero. The developed theory adequately explains the experimental results. We show that the theoretical approach used in this work is equivalent to the one applied in the Brownian dynamics simulation work performed by Porschke and co-workers. We also analyse the effect of a possible electric dipole moment on the transients of the reduced electric linear dichroism in DNA bent fragments.