  We examine the eccentricity evolution of a system of two planets locked in a
mean motion resonance, in which the outer planet loses energy and angular
momentum. The sink of energy and angular momentum could be either a gas or
planetesimal disk. We show that the eccentricity of both planetary bodies can
grow to large values, particularly if the inner body does not directly exchange
energy or angular momentum with the disk. We analytically calculate the
eccentricity damping rate in the case of a single planet migrating through a
planetesimal disk. We present the results of numerical integrations of two
resonant planets showing rapid growth of eccentricity. We also present
integrations in which a Jupiter-mass planet is forced to migrate inward through
a system of 5-10 roughly Earth mass planets. The migrating planet can eject or
accrete the smaller bodies; roughly 5% of the mass (averaged over all the
integrations) accretes onto the central star. The results are discussed in the
context of the currently known extrasolar planetary systems.
