We survey the linear viscoelasticity of a new type of transient network: bridged wormlike micelles, whose structure has been characterized recently by Ramos and Ligoure [Macromolecules 40, 1248-1251 (2007)]. This composite material is obtained by adding telechelic copolymers (water-soluble chains with hydrophobic stickers at each extremity) to a solution of entangled wormlike micelles (WM). For comparison, naked WM and WM decorated by amphiphilic copolymers are also investigated. While these latter systems exhibit almost a same single ideal Maxwell behavior, solutions of bridged WM can be described as two Maxwell fluids component blends, characterized by two markedly different characteristic timesT(fast) and T-slow, and two elastic moduli, G(fast) and G(slow), with G(fast) >> G(slow). We show that the slow mode is related to the viscoelasticity of the transient network of entangled WM, and the fast mode to the network of telechelic active chains (i.e., chains that do not form loops but bridge two micelles). The dependence of the viscoelasticity with the surfactant concentration, phi, and the sticker-to-surfactant molar ratio, beta, is discussed. In particular, we show that G(fast) is proportional to the number of active chains in the material, phi beta. Simple theoretical expectations then allow evaluation of the bridges/loops ratio for the telechelic polymers. (C) 2008 The Society of Rheology.