The elongation and subsequent relaxation of dilute polyisobutylene solutions in mixtures of polybutene and kerosene have been investigated using a filament stretching device first introduced by Tirtaatmadja and Sridhar [J. Rheol., 37 (1993) 1081-1102]. A novel experimental technique has been developed which enables the nature of the total stress measured by experiment to be investigated. A sudden decrease in stress is observed on cessation of the extensional flow. This is followed by a much slower relaxation. The results can be interpreted in terms of viscous and elastic stresses. An alternative explanation in terms of the dumbbell model is also explored. The viscous stresses were observed to scale with strain rate at any given value of chain extension, whilst at steady state, the elastic stresses remained constant over a range of strain rates. Computations using a FENE-P model, with parameters evaluated from steady shear data, are shown to predict the growth of the elastic stress component. The same model seems to predict the relaxation of stresses reasonably well. A new stretching technique has also been developed which allows excellent agreement between radially and axially computed strain rates, indicating homogeneous defomation of the fluid sample.