In a nonpolar solvent such as benzene (Bz), living anionic chains having Li as the countercations generally aggregate with each other through Li at their ends. Specifically, the bianionic chains having Li at both ends form an aggregated network, For investigation of the dynamics of the aggregates, polybutadienyl dilithium (PBLi2) bianionic chains were polymerized in Bz, and their viscoelastic behavior was examined in a vacuum with a magnetically floating ball rheometer. This rheometer magnetically kept a position of a steel ball in a flowing liquid contained in a glass cell (test tubing) and measured a force acting on the ball, and the viscosity was obtained from this force. The viscoelastic relaxation after cessation of the flow was also detected as a decay of the force. In the experiment for the living PBLi2/Bz solution, the deactivation of the PB bianions was avoided by coating the steel ball with a nonreactive polyethylene film and by rinsing the cell with a Bz solution of diphenylethlenyllithium before the PBLi2/Bz solution was vacuum-sealed in it. The zero-shear viscosity eta(0)((anion)) and terminal relaxation time tau(1)((anion)) of the living PB bianionic chains of the molecular weight = 14 x 10(3) and concentration = 2.2 wt %, measured at several temperatures T less than or equal to 30 degreesC, were orders of magnitude larger than those of the same chains deactivated with methanol. This result confirmed that the PB bianionic chains aggregated into a transient network. Thus, the viscoelastic was assigned as the lifetime of the Li aggregates sustaining the network. The lifetime independently estimated from Li-7 NMR data was close to tau(1)((anion)) lending support to this assignment of tau(1)((anino)). Furthermore, the analysis of the viscoelastic relaxation intensity suggested that only a small fraction (congruent to2%) of the PB chains formed the large transient network and the majority of the chains formed smaller aggregates.