  We consider N identical oscillators coupled to a single environment and show
that the conditions for the existence of decoherence free subspaces are
degeneracy of the oscillator frequencies and separability of the coupling with
the environment. A formal exact equation for the evolution in the case of two
oscillators is found and the decoherence free subspace is explicitly
determined. A full analytical solution for any initial condition and general
parameters (frequencies and dissipation constants) is given in the markovian
approximation and zero temperature. We find that slight relaxation of
degeneracy and separability conditions leads to the appearence of two
components in the dynamical evolution with very different decoherence times.
The ratio between the characteristic time of the weak and strong decoherent
components is given by $\tau_{WD}/\tau_{SD}\approx k/\delta k$, where $\delta
k$ is a measure of the nonseparability of the coupling to the environment and
$k$ is the mean decay constant of the oscillators.
