  The recently introduced notions of guarded traced (monoidal) category and
guarded (pre-)iterative monad aim at unifying different instances of partial
iteration whilst keeping in touch with the established theory of total
iteration and preserving its merits. In this paper we use these notions and the
corresponding stock of results to examine different types of iteration for
hybrid computations. As a starting point we use an available notion of hybrid
monad restricted to the category of sets, and modify it in order to obtain a
suitable notion of guarded iteration with guardedness interpreted as
progressiveness in time - we motivate this modification by our intention to
capture Zeno behaviour in an arguably general and feasible way. We illustrate
our results with a simple programming language for hybrid computations and
interpret it over the developed semantic foundations.
