This paper investigates the testing of weak cross-sectional dependence in large panels using the exponent of cross-sectional dependence introduced by Bailey, Kapetanios, and Pesaran (2012). It shows that the implicit null hypothesis of the cross-sectional dependence (CD) test depends on the relative expansion rates of N (cross-sectional dimension) and T (time dimension). In large N panels, the null hypothesis of weak dependence is more appropriate than the null of independence, which can be restrictive for large panels. The CD test is shown to have correct size for values of the cross-sectional exponent in the range [0, 1/4] for all combinations of N and T, regardless of whether the panel contains lagged values of the dependent variables, as long as there are no major asymmetries in the error distribution. The CD test is also shown to have satisfactory power for all values of the cross-sectional exponent greater than 1/2. The paper also discusses the asymptotic distribution of the CD test under the null of weak cross-sectional dependence and shows that it tends to N(0,1) under certain conditions. The CD test is applied to heterogeneous dynamic panels and is shown to have good small sample properties. The paper concludes that the CD test is a valid and powerful test for weak cross-sectional dependence in large panels.This paper investigates the testing of weak cross-sectional dependence in large panels using the exponent of cross-sectional dependence introduced by Bailey, Kapetanios, and Pesaran (2012). It shows that the implicit null hypothesis of the cross-sectional dependence (CD) test depends on the relative expansion rates of N (cross-sectional dimension) and T (time dimension). In large N panels, the null hypothesis of weak dependence is more appropriate than the null of independence, which can be restrictive for large panels. The CD test is shown to have correct size for values of the cross-sectional exponent in the range [0, 1/4] for all combinations of N and T, regardless of whether the panel contains lagged values of the dependent variables, as long as there are no major asymmetries in the error distribution. The CD test is also shown to have satisfactory power for all values of the cross-sectional exponent greater than 1/2. The paper also discusses the asymptotic distribution of the CD test under the null of weak cross-sectional dependence and shows that it tends to N(0,1) under certain conditions. The CD test is applied to heterogeneous dynamic panels and is shown to have good small sample properties. The paper concludes that the CD test is a valid and powerful test for weak cross-sectional dependence in large panels.