In this work, Bayesian and non-Bayesian estimators have been obtained for two-parameter exponentiated Weibull distribution when sample is available from single hybrid censoring scheme and hybrid progressive censored scheme. Besides, the maximum likelihood estimators of the parameters and the asymptotic variance covariance matrix have been also obtained. Bayes estimators have been developed under squared error loss function as well as under LINEX loss function using non-informative type of priors for the parameters. A numerical illustration for these new results is given.