Typically, we think of a shoreline growing with a smooth line separating the land and the water. If the growth is unstable, however, the land–water front will exhibit a roughness that grows with time. Here we ask whether the growth of deltaic shorelines cab be unstable. Through mathematical analysis we show that growth is unstable when the shoreline is building onto an adverse slope. The length scale of the unstable signal in such a case, however, might be obscured by other geomorphic processes.