A new model for the linear viscoelastic behavior of polymer networks is developed. In this model the polymer system is described as a network of spring segments connected via sticky points (as in the Lodge model). [Lodge, A. S., “A network theory of flow birefringence and stress in concentrated polymer solutions,” Trans. Faraday Soc. 52, 120–130 (1956).] An important extension (with respect to previous models) is that chain connectivity is taken into account. All segments that are located in between connected stickers are supposed to carry stress. The attachment and detachment of stickers is described with kinetic equations in which activation energies play a role. Simultaneous transitions involving groups of stickers are allowed. The model shows a strong dependence upon the number of segments per chain. Broad relaxation spectra can be obtained. The storage modulus can have more than one plateau corresponding with the fact that stress relaxation may need the breakup of several bonds.