  The time-resolved photoconductance of amorphous and crystalline
LaAlO$_3$/SrTiO$_3$ interfaces, both hosting an interfacial 2-dimensional
electron gas, is investigated under irradiation by variable-wavelengths,
visible or ultraviolet photons. Unlike bare SrTiO$_3$ single crystals, showing
relatively small photoconductance effects, both kinds of interfaces exhibit an
intense and highly persistent photoconductance with extraordinarily long
characteristic times. The temporal behaviour of the extra photoinduced
conductance persisting after light irradiation shows a complex dependence on
interface type (whether amorphous or crystalline), sample history and
irradiation wavelength. \textcolor{black}{The experimental results indicate
that different mechanisms of photoexcitation are responsible for the
photoconductance of crystalline and amorphous LaAlO$_3$/SrTiO$_3$ interfaces
under visible light. We propose that the response of crystalline samples is
mainly due to the promotion of electrons from the valence bands of both
SrTiO$_3$ and LaAlO$_3$. This second channel is less relevant in amorphous
LaAlO$_3$/SrTiO$_3$, where the higher density of point defects plays instead a
major role.
