We report on a study of pi and eta decays of strange baryon resonances within relativistic constituent-quark models based on one-gluon-exchange and Goldstone-boson-exchange dynamics. The investigations are performed in the point form of Poincare-invariant relativistic quantum mechanics with a spectator-model decay operator. The covariant predictions of the constituent-quark models underestimate the experimental data in most cases. These findings are congruent with an earlier study of nonstrange baryon decays in the light-flavor sector. We also consider a nonrelativistic reduction of the point-form spectator model, which leads to the decay operator of the elementary emission model. For some decays the nonrelativistic results differ substantially from the relativistic ones and they exhibit no uniform behavior as they scatter above and below the experimental decay widths.