  We present new solutions to Einstein-Maxwell-dilaton-axion (EMDA) gravity in
four dimensions describing black holes which asymptote to the linear dilaton
background. In the non-rotating case they can be obtained as the limiting
geometry of dilaton black holes. The rotating solutions (possibly endowed with
a NUT parameter) are constructed using a generating technique based on the
Sp(4,R) duality of the EMDA system. In a certain limit (with no event horizon
present) our rotating solutions coincide with supersymmetric
Israel-Wilson-Perjes type dilaton-axion solutions. In presence of an event
horizon supersymmetry is broken. The temperature of the static black holes is
constant, and their mass does not depend on it, so the heat capacity is zero.
We investigate geodesics and wave propagation in these spacetimes and find
superradiance in the rotating case. Because of the non-asymptotically flat
nature of the geometry, certain modes are reflected from infinity, in
particular, all superradiant modes are confined. This leads to classical
instability of the rotating solutions. The non-rotating linear dilaton black
holes are shown to be stable under spherical perturbations.
