Solutions of bimetallic tetracarboxylates (M2R4) in apolar hydrocarbons have been studied. They contain thin monomolecular threads and exhibit behaviors reminiscent of breakable giant micelles entangled in transient networks. Nonlinear theology and anisotropic small-angle neutron scattering patterns characterize a "shear-banding" phenomenon. Analysis is made in the framework of ideal Maxwellian systems. It is shown that the viscoelasticity can be controlled by using specific end cappers. The dramatic influence of both the metal and aliphatic tail upon the theological properties is illustrated.