  We study the evolution of streams in a time-dependent spherical gravitational
potential. Our goal is to establish what are the imprints of this time
evolution on the properties of streams as well as their observability. To this
end, we have performed a suite of numerical experiments for a host system that
doubles its mass during the integration time and for a variety of initial
conditions. In these experiments we found that the most striking imprint is a
misalignment of 10 degrees in the angular location of the apocentres of the
streams compared to the static case (and to the orbit of the centre of mass),
which only becomes apparent for sufficiently long streams. We have also
developed an analytic model using action-angle variables which allows us to
explain this behaviour and to identify the most important signature of time
evolution, namely a difference in the slope defined by the distribution of
particles along a stream in frequency and in angle space. Although a difference
in slope can arise when the present-day potential is not correctly modelled,
this shortcoming can be by-passed because in this case, streams are no longer
straight lines in angle space, but depict a wiggly appearance and an
implausible energy gradient. The difference in slope due to time-evolution is
small, typically $\sim10^{-2}$ and its amplitude depends on the growth rate of
the potential, but nonetheless we find that it could be observable if accurate
full-space information for nearby long streams is available.
