  We present the results of a high-resolution imaging survey for brown dwarf
(BD) binaries in two open clusters. The observations were carried out with
WFPC2 onboard HST. Our sample consists of 8 BD candidates in the alpha Per
cluster and 25 BD candidates in the Pleiades. We have resolved 4 binaries in
the Pleiades with separations in the range 0".094--0".058, corresponding to
projected separations between 11.7~AU and 7.2~AU. No binaries were found among
the alpha Per targets. Three of the binaries have proper motions consistent
with cluster membership in the Pleiades cluster, and for one of them we report
the detection of Halpha in emission and LiI absorption obtained from
Keck~II/ESI spectroscopy. One of the binaries does not have a proper motion
consistent with Pleiades membership. We estimate that BD binaries wider than
12~AU are less frequent than 9% in the alphaPer and Pleiades clusters. This is
consistent with an extension to substellar masses of a trend observed among
stellar binaries: the maximum semimajor axis of binary systems decreases with
decreasing primary mass. We find a binary frequency of 2 binaries over 13 BDs
with confirmed proper motion membership in the Pleiades, corresponding to a
binary fraction of 15%(1 sigma error bar +15%/-5%). These binaries are limited
to the separation range 7-12~AU and their mass ratios are larger than 0.7. The
relatively high binary frequency (>10%), the bias to separations smaller than
about 15 AU and the trend to high mass ratios (q>0.7) are fundamental
properties of BDs. Current theories of BD formation do not appear to provide a
good description of all these properties.
