Low-density polyethylene was thermally and thermo-oxidatively degraded at 170 degrees C and subsequently characterized by linear-viscoelastic measurements and in uniaxial extension. The elongational viscosities measured were analyzed in the framework of the Molecular Stress Function (MSF) model. For the thermally degraded samples, degradation times between 2 and 6 h were applied. Formation of long-chain branching (LCB) evidenced by enhanced strain hardening was found to occur only during the first 2 h of thermal degradation. At longer exposure times, no difference in the level of strain hardening was observed. This was quantified by use of the MSF model, which in elongation has two-model parameters: f(max)(2) determining the maximum relative stretch of the chain segments, and beta representing the ratio of the molar mass of the (branched) polymer chain to the molar mass of the effective backbone alone. The non-linear parameter f(max)(2) increased from f(max)(2) = 14 for the non- degraded sample to f(max)(2) = 22 for the samples thermally degraded for 2 up to 6 h. For the thermo- oxidatively degraded samples, i. e. those degraded in the presence of air, degradation times between 30 and 90 min were applied. Surprisingly, under these degradation conditions, the level of strain hardening increases drastically up to f(max)(2) = 55 with increasing exposure times from 30 up to 75 min due to LCB formation and then decreases for an exposure time of 90 min due to chain scission dominating LCB formation. The non-linear parameter beta of the MSF model was found to be beta = 2 for all samples, indicating that the general type of the random branching structure remains the same under all degradation conditions. Consequently, only the parameter f(max)(2) of theMSF model and the linear- viscoelastic spectra were required to describe quantitatively the experimental observations. The strain hardening index, which is sometimes used to quantify strain hardening, was shown to follow accurately the trend of the MSF model parameter f(max)(2).