Simple deterministic systems are capable of generating chaotic output that "mimics" the output of stochastic systems. For this reason, algorithms have been developed to distinguish between these two alternatives. These algorithms and related statistical tests are also useful in detecting the presence of nonlinear dependence in time series. In this article, the authors apply these procedures to stock returns and find evidence that indicates the presence of nonlinear dependence on weekly returns from the Center for Research in Security Prices value-weighted index. Copyright 1989 by the University of Chicago.