  We have investigated the dynamical stability of the proposed companions
orbiting the Algol type short-period eclipsing binary SW Lyncis (Kim et al.
2010). The two candidate companions are of stellar to sub-stellar nature, and
were inferred from timing measurements of the system's primary and secondary
eclipses. We applied well-tested numerical techniques to accurately integrate
the orbits of the two companions and to test for chaotic dynamical behaviour.
We carried out the stability analysis within a systematic parameter survey
varying both the geometries and orientation of the orbits of the companions, as
well as their masses. In all our numerical integrations we found that the
proposed SW Lyn multi-body system is highly unstable on time-scales on the
order of 1000 years. Our results cast doubt on the interpretation that the
timing variations are caused by two companions. This work demonstrates that a
straightforward dynamical analysis can help to test whether a best-fit
companion-based model is a physically viable explanation for measured eclipse
timing variations. We conclude that dynamical considerations reveal that the
propsed SW Lyncis multi-body system most likely does not exist or the
companions have significantly different orbital properties as conjectured in
Kim et al. (2010).
