  We investigate time-dependent spherically symmetric solutions of the
four-dimensional Einstein-Maxwell-axion-dilaton system, with the dilaton
coupling that occurs in low-energy effective heterotic string theory. A class
of dilaton-electrovacuum radiating solutions with a trivial axion, previously
found by G\"uven and Y\"or\"uk, is re-derived in a simpler manner and its
causal structure is clarified. It is shown that such dynamical spacetimes
featuring apparent horizons do not possess a regular light-like past null
infinity or future null infinity, depending on whether they are radiating or
accreting. These solutions are then extended in two ways. First we consider a
Vaidya-like generalisation, which introduces a null dust source. Such
spacetimes are used to test the status of cosmic censorship in the context of
low-energy string theory. We prove that - within this family of solutions -
regular black holes cannot evolve into naked singularities by accreting null
dust, unless standard energy conditions are violated. Secondly, we employ
S-duality to derive new time-dependent dyon solutions with a nontrivial axion
turned on. Although they share the same causal structure as their
Einstein-Maxwell-dilaton counterparts, these solutions possess both electric
and magnetic charges.
