  As the Universe expands, the redshift of distant sources changes with time.
Here we discuss gravitational lensing phenomena that are consequence of the
redshift drift between lensed source, gravitational lens, and observer. When
the source is located very close to the drifting caustics, a pair of images
could occur (or disappear) because of the cosmological expansion. Furthermore,
lensing systems act as signal converters of the redshift drift. The angular
position, magnification, distortion, and time delay of already existing
multiple images change. We estimate the expected frequency of these phenomena
and the prospects to observe them in the era of deep and large surveys. The
drift detection in image separation could be within reach of next generation
surveys with $\mu$arcsec angular resolution.
