  We discuss some aspects of higher-dimensional gravitational solitons and
kinks, including in particular their stability. We illustrate our discussion
with the examples of (non-BPS) higher-dimensional Taub-NUT solutions as the
spatial metrics in (6+1) and (8+1) dimensions. We find them to be stable
against small but non-infinitesimal disturbances, but unstable against large
ones, which can lead to black-hole formation. In (8+1) dimensions we find a
continuous non-BPS family of asymptotically-conical solitons connecting a
previously-known kink metric with the supersymmetric A_8 solution which has
Spin(7) holonomy. All the solitonic spacetimes we consider are topologcally,
but not geometrically, trivial. In an appendix we use the techniques developed
in the paper to establish the linear stability of five-dimensional Myers-Perry
black holes with equal angular momenta against cohomogeneity-2 perturbations.
