We here suggest a new Brownian dynamics algorithm for telechelic associating polymers with the aim of better understanding the complex rheological behavior of these systems and in particular of hydrophobically modified ethoxylated urethane solutions showing strain hardening in shear startup and significant deviations from the Cox-Merz rule (including shear thickening phenomena). Several molecular mechanisms have indeed been suggested to explain such a complex behavior, ranging from finite extensible nonlinear elasticity (FENE) effects, shearinduced increased association, and, very recently, flow-induced repulsive interactions between colliding flower-like micelles. The preliminary results here reported (only exploring a limited range of the wide parameter space) appear to suggest that FENE effects are mostly responsible for strain hardening, while deviations from the Cox-Merz rule are due to the persistence of bridge chains, as well as, in some cases, to the flow-induced formation of new bridges. In the explored parameter space, no significant role appears to be played by flowinduced collisions between micelles beyond that of preventing network collapse. (C) 2017 The Society of Rheology.