  In this paper we investigate quasi-stationary distributions {\mu}_N of
stochastic approximation algorithms with constant step size which can be viewed
as random perturbations of a time-continuous dynamical system. Inspired by
ecological models these processes have a closed absorbing set corresponding to
extinction. Under some large deviation assumptions and the existence of an
interior attractor for the ODE, we show that the weak* limit points of the QSD
{\mu}_N are invariant measures for the ODE with support in the interior
attractors.
