  We present ESO NTT high resolution echelle spectroscopy of the central stars
(CSs) of eight southern bipolar planetary nebulae (PNe) selected for their
asymmetry. Our aim was to determine or place limits on the magnetic fields of
the CSs of these nebulae, and hence to explore the role played by magnetic
fields in nebular morphology and PN shaping. If magnetic fields do play a role,
we expect these CSs to have fields in the range $10^2 - 10^7$ G from magnetic
flux conservation on the reasonable assumption that they must evolve into the
high field magnetic white dwarfs. We were able to place an upper limit of
$\approx 20,000$ G to the magnetic fields of the central stars of He 2-64 and
MyCn 18. The spectrum of He 2-64 also shows a P-Cygni profile in \ion{He}{1}
$\lambda$5876 and $\lambda$6678, corresponding to an expanding photosphere with
velocity $\sim$ 100 km s$^{-1}$. The detection of helium absorption lines in
the spectrum of He 2-36 confirms the existence of a hot stellar component. We
did not reach the necessary line detection for magnetic field analysis in the
remaining objects. Overall, our results indicate that if magnetic fields are
responsible for shaping bipolar planetary nebulae, these are not required to be
greater than a few tens of kilogauss.
