  We study the set of strictly periodic points in surjective cellular automata,
i.e., the set of those configurations which are temporally periodic for a given
automaton but they not spatially periodic. This set turns out to be dense for
almost equicontinuous surjective cellular automata while it is empty for the
positively expansive ones. In the class of additive cellular automata, the set
of strictly periodic points can be either dense or empty. The latter happens if
and only if the cellular automaton is topologically transitive.
