  We derive the complete covariant action for the type IIA superstring in a
simple D=10 background which represents a 7-brane with a magnetic Ramond-Ramond
vector field (and is U-dual to the Kaluza-Klein Melvin solution). This curved
background can be obtained by dimensional reduction from a flat (but
topologically non-trivial) D=11 space-time. The action of a supermembrane
propagating in this flat D=11 space is straightforward to write down. The
explicit form of the superstring action is then obtained by double dimensional
reduction of the supermembrane action. In the light-cone gauge the action
contains only quadratic and quartic terms in fermions.
