We derive a common linear representation for the densities of four generalizations of the two-parameter Weibull distribution in terms of Weibull densities. The four generalized Weibull distributions briefly studied are: the Marshall-Olkin-Weibull, beta-Weibull, gamma-Weibull and Kumaraswamy-Weibull distributions. We demonstrate that several mathematical properties of these generalizations can be obtained simultaneously from those of the Weibull properties. We present two applications to real data sets by comparing these generalized distributions. It is hoped that this paper encourage developments of further generalizations of the Weibull based on the same linear representation.