We have developed and tested a new model suitable for the prediction of linear viscoelasticity (LVE) from knowledge of molecular structure for arbitrary mixtures of polydisperse star and linear entangled molecules. The model is based on key ingredients of tube models: reptation, fluctuations and constraint release. We impose no artificial time scale separation between fluctuations and reptation but rather allow both relaxation processes to proceed simultaneously. Early fluctuations are treated in a new and simple way, based on thermal energy threshold considerations. Because the modelled systems are arbitrary mixtures of linear and star molecules, we cannot obtain analytical solutions but have to resort to a time-marching algorithm to predict the relaxation modulus. The model has been tested on a wide range of literature data. Excellent predictions are obtained if the constraint release solvent influence on relaxation processes is treated consistently by using an extension of the "Graessley criterion". The solvent must be included only if the corresponding constraint release characteristic time is short compared to the considered relaxation process. (c) 2005 Elsevier B.V. All rights reserved.