  We formulate a set of linear equations that describe the behaviour of small
eccentricities in a protoplanetary system consisting of a gaseous disc and a
planet. Eccentricity propagates through the disc by means of pressure and
self-gravity, and is exchanged with the planet via secular interactions.
Excitation and damping of eccentricity can occur through Lindblad and
corotation resonances, as well as viscosity. We compute normal modes of the
coupled disc-planet system in the case of short-period giant planets orbiting
inside an inner cavity, possibly carved by the stellar magnetosphere.
Three-dimensional effects allow for a mode to be trapped in the inner parts of
the disc. This mode can easily grow within the disc's lifetime. An eccentric
mode dominated by the planet can also grow, although less rapidly. We compute
the structure and growth rates of these modes and their dependence on the
assumed properties of the disc.
