Dynamic light scattering measurements are made on viscoelastic networks formed by threadlike micelles of cetyltrimethylammonium bromide (CTAB) in aqueous sodium salicylate (NaSal) solutions at three temperatures T of 25, 33, and 40 degrees C. Dynamic shear moduli of the same samples are also measured in the angular frequency range from 1 x 10(-2) to 1 x 10(2) rad s(-1) at T=25, 33, 40, 50, and 60 degrees C. The surfactant concentration C-D of the samples is fixed at 0.1 M and a ratio of the salt concentration C-S to C-D is varied from 0.8 to 6. The time correlation function A(q)(t) of light intensity scattered from the solutions with 0.8 less than or equal to C-S/C-D less than or equal to 4 exhibits the bimodal distribution of the decay rate Gamma. The fast and the slowly decaying components are assigned as the diffusive gel mode and the relaxation mode, respectively, from the scattering vector dependences of the first cumulant Gamma(i) (i=f, s) estimated from respective time profiles of the decay curves at short and long times. The dynamical correlation length xi(H) calculated from D-c = Gamma(f)/q(2) is found to take a constant value of 10.5 +/- 1.5 nm irrespective of C-S/C-D and T for 1 less than or equal to C-S/C-D I 6. The characteristic relaxation time tau(s) (=Gamma(s)(-1)) for the slow mode agrees with the mechanical relaxation time tau(M) which is obtained by a fit of the dynamic shear modulus data of the same solutions to a Maxwell model with the single relaxation time tm. The results demonstrate that concentration fluctuation in the micellar network decays by local cooperative diffusion of network strands at the short time as well as by the slow relaxation of elastic stress generated by the network deformation due to the mass flow.