A network model for polymer melts is presented in which disentangled strands relax under flow conditions and may rejoin the network before complete relaxation. For simplicity, we study Gaussian strands that move affinely when incorporated in the network. Network strands are created and lost according to a time constant lambda. Free strands have their dynamics given by the Bird-DeAguiar model as a crude representation of reptation and the hindered rotation experienced by polymer strands in melts. The model yields a shear-thinning viscosity with overshoot in the start-up viscosity eta(+) (t). The double-step strain results compare well with available experimental data.