Dynamical properties of propagating baroclinic bottom–intensified eddies on a sloping bottom are investigated. The model is based on one previously introduced describing the sub–inertial dynamics of density–driven flows on a sloping bottom within a continuously stratified rotating fluid. A variational principle is established for arbitrary nonlinear steadily travelling eddies. Explicit solutions are obtained for fully nonlinear radially symmetric eddies. The eddies correspond to a bottom–trapped cold dome that has a predominantly anticyclonic circulation within it and a relatively strong cyclonic eddy in the overlying fluid, which satisfies the Mory–Stern isolation constraint. These eddies are able to transport bottom- and intermediate–water fluid parcels. An approximate solution is also constructed for a radiating cold dome. These eddies possess a topographic Rossby wave field behind the travelling eddy. The associated wave drag results in down–slope motion into deeper waters. The theoretical work is illustrated with a specific solution for a cold dome with a parabolic height profile that intersects the bottom.