  We consider delay differential equations (DDE) that are on the verge of an
instability, i.e. the characteristic equation for the linearized equation has
one root as zero and all other roots have negative real parts. In presence of
small mean-zero noise, we study the large deviations from the corresponding
deterministic system. Using spectral theory for DDE it is easy to see that, the
projection on to the one dimensional space corresponding to the zero root is
exponentially equivalent with the original process. For the one-dimensional
process we make the observation that the results of Freidlin-Wentzell apply.
