  In [1], the authors have studied stability of certain causal properties of
space-times in general relativity. As a continuation of this work, in the
present paper, we review and discuss, some more aspects of stability which
occur in various situations in the dynamics of general relativity. We argue
that not only choice of appropriate topology, but also the nature of
perturbation, like metric, matter or initial data, are key factors in deciding
whether a property is stable or not. We also study certain properties of
space-times which are generic in an appropriate mathematical sense. In
particular we argue that Linearization stability of a space-time is a generic
property.
