  We investigate the properties of the AdS D1-branes which are the bound states
of a curved D1-brane with $n$ fundamental strings (F1) in the $AdS_3$
spacetime, and the AdS D2-branes which are the axially symmetric bound states
of a curved D2-brane with $m$ D0-branes and $n$ fundamental strings in the
$AdS_3 \times S^3$ spacetime. We see that, while the AdS D1-branes
asymptotically approach to the event horizon of the $AdS_3$ spacetime the AdS
D2-branes will end on it. As the near horizon geometry of the F1/NS5 becomes
the spacetime of $AdS_3 \times S^3 \times T^4$ with NS-NS three form turned on,
we furthermore investigate the corresponding AdS D-branes in the NS5-branes and
macroscopic F-strings backgrounds, as an attempt to understand the origin of
the AdS D-branes. From the found DBI solutions we see that in the F-strings
background, both of the AdS D1-branes and AdS D2-branes will asymptotically
approach to the position with a finite distance away from the F-strings.
However, the AdS D2-branes therein could also end on the F-strings once it
carries sufficient D0-branes charges. We also see that there does not exist any
stable AdS D-branes in the NS5-branes backgrounds. We present physical
arguments to explain these results, which could help us in understanding the
intriguing mechanics of the formation of the AdS D-branes.
