  A multimode uncertainty relation (generalising the Robertson-Schroedinger
relation) is derived as a necessary constraint on the second moments of n pairs
of canonical operators. In turn, necessary conditions for the separability of
multimode continuous variable states under (m+n)-mode bipartitions are derived
from the uncertainty relation. These conditions are proven to be necessary and
sufficient for (1+n)-mode Gaussian states and for (m+n)-mode bisymmetric
Gaussian states.
