Wormlike micelles (WLMs) are polymer-like chains formed by surfactant self-assembly in water. Recently, we have shown that WLMs can also be self-assembled in polar organic liquids like glycerol using a cationic surfactant and an aromatic salt. In this work, we focus on the dynamic rheology of the WLMs in glycerol and demonstrate that their rheology is very different from that of WLMs in water. Aqueous WLMs that are entangled into transient networks exhibit the rheology of a perfect Maxwell fluid having a single relaxation time t(R)-thereby, their elastic modulus G' and viscous modulus G '' intersect at a crossover frequency omega(c) = 1/t(R). WLMs in glycerol also form entangled networks, but they are not Maxwell fluids; instead, they exhibit a double-crossover of G' and G '' (at omega(c1) and omega(c2)) within the w-window accessible by rheometry (10(-2) to 10(2) rad/s). The first crossover at omega(c1) (similar to 1 rad/s) corresponds to the terminal relaxation time (i.e., the timescale for chains to disentangle from the transient network and relax by reptation). At the other extreme, at frequencies above omega(c2) (which is similar to 10 rad/s), the rheology is dominated by the segmental motion of the chains. This "breathing regime" has rarely been accessed via experiments for aqueous WLMs because it falls around 10(5) rad/s. We believe that glycerol, a solvent that is much more viscous than water, exerts a crucial influence in pushing omega(c2) to 1000-fold lower frequencies. On the basis of the rheology, we also hypothesize that WLMs in glycerol are shorter and weakly entangled compared to WLMs in water. Moreover, we suggest that WLMs in glycerol are "unbreakable" chains-i.e., the chains remain mostly intact instead of breaking and re-forming frequently-and this polymer-like behavior explains why the samples are quite unlike Maxwell fluids.