Estimations of the parameters included in a competing risks model in the presence of incomplete and censored data are discussed in this paper. The case when the competing risks have generalized Weibull distributions is considered. We derive both point and asymptotic confidence interval estimations of the parameters included in the model using the maximum likelihood procedure. The relative risks due to each cause of failure are investigated. We apply the theoretical results obtained in this paper on a set of real data. Also, we study hypothesis tests to investigate if the real data set we used can be fitted well by the generalized Weibull distribution.