Strong approximation for the deviation of kernel copula estimators

We prove a uniform in bandwidth law of the iterated logarithm for the maximal deviation of kernel copula estimators from their expectations. We deal especially with the $\mathit{\text{local}}\mathit{\text{linear}}$, the $\mathit{\text{mirror-reflection}}$ and the $\mathit{\text{transformation}}$ estimators. These results are useful for establishing the strong uniform in bandwidth consistency of these kernel estimators.