  Decoherence free subspaces (DFS) is a theoretical tool towards experimental
implementation of quantum information storage and processing. However, they
represent an experimental challenge, since conditions for their existence are
very stringent. This work explores the situation in which a system of $N$
oscillators coupled to a bath of harmonic oscillators is close to satisfy the
conditions for the existence of DFS. We show, in the Born-Markov limit and for
small deviations from separability and degeneracy conditions, that there are
{\emph{weak decoherence subspaces}} which resemble the original notion of DFS.
