Stable wrapped branes

We study some wrapped configurations of branes in the near-horizon geometry of a stack of other branes. The common feature of all the cases analyzed i s a quantization rule and the appearance of a finite number of static confi gurations in which the branes are partially wrapped on spheres. The energy of these configurations can be given in closed form and the analysis of the ir small oscillations shows that they are stable. The cases studied include D(8 - p)-branes in the type-II supergravity background of Dp-branes for 0 less than or equal to p less than or equal to 5, M5-branes in the M5-brane geometry in M-theory and D3-branes in a (p, q) fivebrane background in the type-IIB theory. The brane configurations found admit the interpretation of bound states of strings (or M2-branes in M-theory) which extend along the unwrapped directions. We check this fact directly in a particular case by u sing the Myers polarization mechanism.