Consider a circle of devices, each characterized by a one-bit output which is statistically correlated with the outputs of its right and/or left neighbor at the preceding time period. It is shown that, provided no input-output relation is deterministic, this system will eventually become completely disorganized in the sense that it will behave like a collection of independent parts with completely unpredictable behavior. The rate at which this disorganization occurs under various conditions is calculated. A concrete version of this model is a sequential circuit of imperfect relays. A possible application to the determination of certain reliability parameters is given. The relation to a similar model for statistical mechanics by Kac is shown. © 1959 Academic Press, Inc.