In this article we study the application of nonlinear indices (sometimes called complexity indices) to univariate time series data arising from studies of schizophrenia and bipolar disorder. Specifically, we consider time series arising from EEG studies, ECG studies, and self-report mood data. As part of our analysis, we empirically examine the claim in the literature that complexity tends to be higher in the EEG of schizophrenia patients than controls and that this tendency is dampened or even inverted by medication, increasing age, and reduced symptomatology. Our conclusion is that this claim is only partially supported and propose that symptomatology, specifically the presence or absence of schizophrenia 'deficit syndrome,' may be the most important factor. Results are more consistent in ECG studies in which reduced heart rate complexity is observed in both schizophrenia and bipolar disorder. The applications of nonlinear indices to the effects of antipsychotic medication and the discrimination of mood states are also examined. It is concluded that the monitoring of nonlinear indices may be useful in predicting response to medication and predicting onset of specific mood states.