A full-chain, temporary network model is proposed for nonlinear flows of linear, entangled polymeric liquids. The model is inspired by the success of a recent reptation model, but contains no beads or tubes. Instead, each chain uses a different (and smaller) set of dynamic variables: the location of each entanglement and the number of Kuhn steps in chain strands between entanglements: As before, the model requires only a single phenomenological parameter that is fit by linear viscoelasticity. The number of Kuhn steps varies stochastically from imbalances in chemical potential and Brownian forces. In the language of reptation, the model exhibits chain connectivity, chain-length fluctuations, chain stretching, and tube dilation. The current implementation in this framework does not include constraint release, although its addition is possible. The entanglements are assumed to move affinely. Because of the affinity assumption and lack of constraint release, the model should be expected to approximate well a linear chain in a matrix of fixed obstacles, and somewhat less accurately a polymer melt. Straightforward modifications to these assumptions allow us to consider chains of any architecture in concentrated solutions or melts. A simulation algorithm for the model is described in detail. Stress results are encouraging, since the model performs at least as well as a complete tube model without constraint release at much lower computational cost. Finally, we consider possible generalizations of the proposed model, to include additional physics, such as constraint release, branching, and nonaffine motion. (C) 2003 The Society of Rheology.