A double-network model is established, which consists of the segments, E and A-constituent chains, the polymeric chains entangled with other ones by multi-entanglement and polymeric chains connected to a great number of destructible particles by multi-adsorption, based on which the E and A-constituent chains can be recreated and released dynamically. The distribution function of the end-to-end vector, the statistical distribution function of conformation for two kinds of chains in the multi-entanglement and multi-adsorption states and their number of polymeric chains are calculated by the combination of statistical mechanics and kinetics. Then the viscoelastic free energies of deformation for two kinds of the networks and suspensions are calculated by Boltzmann’s statistical theory. Also. elastic modulus and memory function for two kinds of the network and suspensions are derived. Consequently, a new molecular theory of the non-linear viscoelasticity for polymeric suspensions is proposed, and the constitutive equation and material function with yielding and thinning for the polymeric suspensions in different flow fields are derived from this theory. A double-network model is established, which consists of the segments, E and A-constituent chains, the polymeric chains entangled with other ones by multi-entanglement and polymeric chains connected to a great number of destructible particles by multi-adsorption, based on which the E and A-constituent chains can be recreated and released dynamically. The distribution function of the end-to-end vector, the statistical distribution function of conformation for two kinds of chains in the multi-entanglement and multi-adsorption states and their number of polymeric chains are calculated by the combination of statistical mechanics and kinetics. Then the viscoelastic free energies of deformation for two kinds of the networks and suspensions are calculated by Boltzmann’s statistical theory. Also. elastic modulus and memory function for two kinds of the network and suspensions are derived. Of, a new molecular theory of the non-linear viscoelasticity for polymeric suspensions is propos ed, and the constitutive equation and material function with yielding and thinning for the polymeric suspensions in different flow fields are derived from this theory.