Lodge's molecular network theories are quite successful in describing the linear viscoelastic behavior of polymer solutions and melts, but cannot account for the rate‐of‐strain dependence of various material functions. By allowing the junction‐creation rate and the probability of loss of junctions to depend on the second invariant of the rate‐of‐strain tensor, more realistic constitutive equations were obtained. Two rheological models are proposed by assuming two different mechanisms for the effect of the rate of strain on the kinetics of the network. The experimental data on three fluids (representative of eight viscoelastic fluids) are used to test the models in various flow situations. For steady simple shearing and small‐amplitude, sinusoidal simple shearing, both model A and model B are capable of fitting the four functions η,−(τ11−τ22),η′, andG′rather well over many decades of shear rate or frequency. For suddenly changing flow experiments model A is inadequate. Model B however appears to be the only rheological equation which can fit simultaneously the steady shear, complex viscosity, stress growth, and stress relaxation functions. For stress growth, the agreement with the experimental data is remarkable, especially after the other models were shown to fail drastically. Finally, an interpretation of the stress growth and relaxation phenomena is given in the light of the modified theory.