AbstractDuring the past few years investigators have found evidence indicating that various time‐series representing business cycles, such as production and unemployment, may be nonlinear. In this paper it is assumed that if the time‐series is nonlinear, then it can be adequately described by a smooth transition autoregressive (STAR) model. The paper describes the application of these models to quarterly logarithmic production indices for 13 countries and ‘Europe’. Tests reject linearity for most of these series, and estimated STAR models indicate that the nonlinearity is needed mainly to describe the responses of production to large negative shocks such as oil price