  We introduce a general characterization of sudden cosmological singularities
and investigate the classical stability of homogeneous and isotropic
cosmological solutions of all curvatures containing these singularities to
small scalar, vector, and tensor perturbations using gauge invariant
perturbation theory. We establish that sudden singularities at which the scale
factor, expansion rate, and density are finite are stable except for a set of
special parameter values. We also apply our analysis to the stability of Big
Rip singularities and find the conditions for their stability against small
scalar, vector, and tensor perturbations.
