This paper discusses tests on time series for the presence of low dimensional deterministic chaos. Empirical applications on U.S. business cycle data are reviewed. Two tasks are necessary to test a time series for (low dimensional) deterministic chaos: (1) dimension must be calculated and shown to be low relative to comparable (psuedo) random numbers; (2) Lyapunov exponents and other measures of local instability must be calculated and show local instability relative to a useful standard. The evidence for low dimensional deterministic chaos in U.S. postwar II GNP data is weak (English). Brock: University of Wisconsin, Madison, Wisconsin. Journal of Economic Literature Classification Numbers: 023, 211, 213.