An entanglement network of thread-like micelles of cetyltrimethylammonium bromide (CTAB) complexed with sodium salicylate (NaSal) in an aqueous solution exhibits profound viscoelasticity that can be modeled with a single Maxwell model with the modulus G(N)0 proportional C(D)2.2C(S)0, and the relaxation time tau-m proportional (C(S)*)-2C(D)0 for low C(S)* and is-proportional-to (C(S)*)-5C(D)0 at high C(S)* (congruent-to C(S)-C(D)) that is the excess Sal-; C(D), the detergent; and C(S), the NaSal concentrations. Replacement of NaSal by salicylic acid (HSal) also leads to the formation of an entanglement network of CTAB:HSal micelles. Its viscoelasticity can now be modelled with two parallel Maxwell models having an slow mode of tau-1 proportional (C(A)*)-2C(D)-2, specific to this system, and a fast mode of tau-2 proportional (C(A)*)-5C(D)0 that is similar to the Maxwell-type mode of the CTAB:NaSal system at high C(S)*. The moduli are G(N)0 = G1 + G2 proportional C(D)2.2 but independent of the HSal C(A) concentration. These results imply that the entanglement network in these solutions relaxes dominantly via the reorganization of the micelles at the entanglement points but not through reptation.