  We study the four dimensional effective action of a system of D6-branes
wrapped on the K3 manifold times a torus, allowing the volume of the internal
manifolds to remain dynamical. An unwrapped brane is at best a Dirac monopole
of the dual R-R sector field to which it couples. After wrapping, a brane is
expected to behave as a BPS monopole, where the Higgs vacuum expectation value
is set by the size of the K3. We determine the moduli space of an arbitrary
number of these wrapped branes by introducing a time dependent perturbation of
the static solution, and expanding the supergravity equations of motion to
determine the dynamics of this perturbation, in the low velocity limit. The
result is the hyper-Kahler generalisation of the Euclidean Taub-NUT metric
presented by Gibbons and Manton. We note that our results also pertain to the
behavior of bound states of Kaluza-Klein monopoles and wrapped NS5-branes in
the T^4 compactified heterotic string.
