Previous multiple-task experiments examining relationships among lateral difference measures have been interpreted as supporting (a) both global and local relationships or (b) local relationships only. The evidence from principle components, correlational, and factor analytic approaches is reviewed with the aim of reconciling the literature. Although a principle component has been reported to which all asymmetries correlate positively, it may not reflect existing null and negative correlations between pairs of measures. All three literatures make clear that such correlations exist, calling into question the reality of a global relationship. In contrast, all three approaches find evidence supporting the reality of local relationships. Factor analytic approaches most fully develop local relationships and permit interpretation in terms of hemispheric processes, but they need to (a) use larger sample sizes, (b) prescreen measures for reliability, and (c) make publicly available the underlying correlational matrices. (C) 1998 Academic Press.