We report on telechelic associating polymers in aqueous solutions that self-assemble into starlike flowers in the dilute regime and develop a fully connected network of flowers above some threshold concentration phi* (similar to 1 wt %). The peculiarity of these telechelics is that the end caps are partially fluorinated. Small-angle neutron scattering has been used to investigate the form and structure factors of the starlike aggregates, and linear rheology was performed in order to identify the viscoelastic features of the physically cross-linked network. Taking advantage of the long network relaxation times, we use step-strain experiments of amplitudes gamma comprised between 0.01 and 3 to explore the nonlinear regime of shear deformations. In the linear regime, the stress relaxation function is well described by a stretched exponential of the form G(t) = G(0) exp(-(t/tau(0))(alpha)), where G(0) is the elastic modulus, to the relaxation time, and a an exponent close to 1 (alpha similar to 0.8). With increasing deformations (gamma > 0.4), the elastic modulus is found to increase (strain hardening) while simultaneously the viscoelastic relaxation time decreases. The strain hardening is interpreted in terms of nonlinear stretching of the elastically active chains whereas the reduction of the relaxation time indicates that the chain breakage probability depends on the chain extensions (or end-to-end distances).