A sensitive spectropolarimetric search for magnetic fields has been ca
rried out on a selection of pulsating white dwarfs of both DAV and DBV
spectral types. Despite multiple epochs and uncertainties as low as s
igma(Be) = 1 kG, the observations succeed only in setting upper limits
for the fields present on G226-29, GD 385, ZZ Ceti, and GD 358. The r
esults are inconsistent with a global magnetic held of the strength su
ggested by the pulsation spectrum of ZZ Ceti, and they approach in sen
sitivity the field inferred as existing on GD 358. However, if, as has
been proposed, magnetic fields can be generated in many white dwarfs
by dynamo action, they could be so tangled in structure as to go undet
ected by direct observational means.