Locally free actions on Lorentz manifolds

If a topological group G acts on a topological space M, then we say that the action is orbit nonproper provided that, for some m(0) is an element of M; the orbit map g --> gm(0) : G --> M is nonproper. In this paper we characterize the connected, simply connected Lie groups that admit a locally free, orbit nonproper action by isometries of a connected Lorentz manifold. We also consider a number of variants on this question.