We introduce new nonparametric independence tests based on Renyi and Tsallis divergence measures and copula density function. These tests reduce the complexity of calculations because they only depend on the copula density. The copula density estimated using the local likelihood probit-transformation method is appropriate for the identification of independence. Also, we present the consistency of the copula-based Renyi and Tsallis divergence measures estimators that are considered as test statistics. A simulation study is provided to compare the empirical power of these new tests with the independence test based on the empirical copula. The simulation results show that the suggested tests outperform in weak dependency. Finally, an application in hydrology is presented.

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