  We explore a spatially homogeneous and isotropic Friedmann-Robertson-Walker
(FRW) universe which is filled with agegraphic dark energy (ADE) with mutual
interaction with pressureless dark matter in the background of Brans-Dicke (BD)
theory. We consider both original and new type of agegraphic dark energy (NADE)
and further assume the sign of the interaction term can change during the
history of the Universe. We obtain the equation of state parameter, the
deceleration parameter and the evolutionary equation for the sign-changeable
interacting ADE and NADE in BD theory. We find that, in both models, the
equation of state parameter, $w_D$, cannot cross the phantom line, although
they can predict the Universe evolution from the early deceleration phase to
the late time acceleration, compatible with observations. We also investigate
the sound stability of these models and find out that both models cannot show a
signal of stability for different model parameters.
