  Here we investigate the cosmic dynamics of Friedmann-Robertson-Walker
universes -- flat spatial sections -- which are driven by nonlinear
electrodynamics (NLED) Lagrangians. We pay special attention to the check of
the sign of the square sound speed since, whenever the latter quantity is
negative, the corresponding cosmological model is classically unstable against
small perturbations of the background energy density. Besides, based on
causality arguments, one has to require that the mentioned small perturbations
of the background should propagate at most at the local speed of light. We also
look for the occurrence of curvature singularities. Our results indicate that
several cosmological models which are based in known NLED Lagrangians, either
are plagued by curvature singularities of the sudden and/or big rip type, or
are violently unstable against small perturbations of the cosmological
background -- due to negative sign of the square sound speed -- or both. In
addition, causality issues associated with superluminal propagation of the
background perturbations may also arise.
