Spatial synchrony in abundance among populations at different locations has been studied for many species. Different statistics have been used as measures of synchrony, and various techniques have been employed to test the hypothesis that there is no synchrony. In this paper we first describe and contrast various measures of synchrony and then discuss testing for no synchrony. Tests that ignore the serial correlation are commonly employed but are incorrect if there is serial correlation present, as is often the case with populations followed over time. Alternative approaches and their limitations are presented including tests based on residuals, adjusted degrees of freedom tests, and bootstrap procedures. We recommend tests based on residuals in a model-based setting. We also discuss some of the difficulties of finding model-free approaches and suggest some methods based on confidence intervals for future study.