In this article, we study the so-called the Weibull Weibull distribution. General explicit expressions for the quantile function, expansion of its density function, ordinary and incomplete moments, moments of the residual and reversed residual lifes, order statistics and Rényi and q–entropies are derived. The model parameters are estimated using the maximum likelihood method. Simulation results are provided to assess the accuracy and performance of the maximum likelihood estimators. The usefulness and flexibility of the Weibull Weibull model are illustrated using real data sets.