Abstract This study investigates the role of capital depreciation in economic fluctuations that may appear in multi-sectoral models of optimal growth. In the standard literature on non-linear optimal dynamics, it has been assumed that capital depreciates completely within a period. This study, in contrast, deals with the case in which capital depreciates slowly (more precisely, only by a certain percentage). We adopt the standard two-sector model with Cobb-Douglas production functions and characterize the dynamics around the stationary state. We derive explicit conditions on parameter values under which cyclical optimal paths appear. These conditions reveal the complexity that slow depreciation adds to multi-sectoral optimal dynamics. The economic interpretation of slow depreciation in multi-sectoral models is also discussed.