  We present simple classical dynamical models to illustrate the idea of
introducing a stochasticity with non-locality into the time variable. For
stochasticity in time, these models include noise in the time variable but not
in the "space" variable, which is opposite to the normal description of
stochastic dynamics. Similarly with respect to non-locality, we discuss delayed
and predictive dynamics which involve two points separated on the time axis.
With certain combinations of fluctuations and non-locality in time, we observe
a ``resonance'' effect. This is an effect similar to stochastic resonance,
which has been discussed within the normal context of stochastic dynamics, but
with different mechanisms. We discuss how these models may be developed to fit
a broader context of generalized dynamical systems where fluctuations and
non-locality are present in both space and time.
