A study of finite-amplitude baroclinic instability for a two-layer system with small but non-zero dissipation is presented. The presence of dissipation, however slight, allows the existence of steady finite-amplitude wave solutions. For sufficiently small friction, however, the steady wave may be unstable if a certain criterion, presented in this paper, is satisfied. Calculations indicate that in such cases a continuous, slow, periodic amplitude pulsation exists which is independent of the initial conditions. Abstract A study of finite-amplitude baroclinic instability for a two-layer system with small but non-zero dissipation is presented. The presence of dissipation, however slight, allows the existence of steady finite-amplitude wave solutions. For sufficiently small friction, however, the steady wave may be unstable if a certain criterion, presented in this paper, is satisfied. Calculations indicate that in such cases a continuous, slow, periodic amplitude pulsation exists which is independent of the initial conditions.