  The quasiregular singularities (horizons) that form in the collision of cross
polarized electromagnetic waves are, as in the linear polarized case unstable.
The validity of the Helliwell-Konkowski stability conjecture is tested for a
number of exact back-reaction cases. In the test electromagnetic case the
conjecture fails to predict the correct nature of the singularity while in the
scalar field and in the null dust cases the aggrement is justified.
