Finite-amplitude dynamics of baroclinic waves are examined in the presence of asymmetric Ekman pumping at the lower and upper boundaries. Both asymptotic and spectral numerical methods are employed. The resulting amplitude equations yield time evolutions that can lead to an eventual equilibration, a regular perpetual vacillation or a chaotic vacillation depending on the actual values of the supercriticality, the dissipation and the stratification parameters and the fundamental zonal wavenumber. Within the limits of strong bottom dissipation and weak supercriticality, the system always eventually equilibrates and the asymptotic results compare favorably with the numerical results. The vacillation is most likely to occur when the bottom dissipation is weak, supercriticality is strong or the viscous asymmetry is high. Vacillatory final states are possible for up to an order of magnitude larger bottom dissipation than predicted by the symmetric configuration, provided the top dissipation is small in comparison.