In several numerical case studies of some typical recycle processes, Luyben reported the "snowball" phenomenon : a small change in a load variable causes a very large change in the recycle flow rate around the system. It is important to note that snowballing is a steady-state phenomenon and has nothing to do with dynamics. It does, however, depend on the structure of the control system as Luyben demonstrated. This paper presents a mathematical analysis of the problem for several typical kinetic systems. In the simple binary first-order case of A --> B, an analytical solution can be found for the recycle flow rate as a function of the fresh feed flow rate and fresh feed composition. Two different control structures are explored. It is shown analytically why the control structure proposed by Luyben prevents snowballing and why the conventional structure results in severe snowballing. Two other kinetic systems are studied numerically : consecutive first-order reactions A --> B --> C and a second-order reaction A + B --> C.