An exponentiated general class (EGC) of distributions was considered as the underlying population of this study. Based on a progressive Type-II censored sample, the maximum likelihood and Bayesian estimation of the parameters, the reliability and hazard rate functions of an EGC were studied. Bayesian estimations were conducted under the squared error and linear-exponential (LINEX) loss functions. The maximum likelihood and Bayes predictors of the life lengths of all censored units in the progressive sample are discussed. In addition, the Bayes predictors of future observables were obtained based on the two-sample prediction. A numerical example is given to illustrate some of the results.