  We present new high-speed, multi-observatory, multi-instrument photometry of
the eclipsing polar UZ For in order to measure precise mid-eclipse times with
the aim of detecting any orbital period variations. When combined with
published eclipse times and archival data spanning ~27 years, we detect
departures from a linear and quadratic trend of ~60 s. The departures are
strongly suggestive of two cyclic variations of 16(3) and 5.25(25) years. The
two favoured mechanisms to drive the periodicities are either two giant
extrasolar planets as companions to the binary (with minimum masses of
6.3(1.5)M(Jupiter) and 7.7(1.2)M(Jupiter)) or a magnetic cycle mechanism (e.g.
Applegate's mechanism) of the secondary star. Applegate's mechanism would
require the entire radiant energy output of the secondary and would therefore
seem to be the least likely of the two, barring any further refinements in the
effect of magnetic fieilds (e.g. those of Lanza et al.). The two planet model
can provide realistic solutions but it does not quite capture all of the
eclipse times measurements. A highly eccentric orbit for the outer planet would
fit the data nicely, but we find that such a solution would be unstable. It is
also possible that the periodicities are driven by some combination of both
mechanisms. Further observations of this system are encouraged.
