Abstract
This paper is concerned with estimating the parameters of the finite mixture of two Weibull distributions based on record values. The Maximum likelihood and Bayes methods of estimation are used. Bayes estimates are obtained for the parameters of the mixture model based on beta conjugate prior for the proportion parameter and gamma conjugate priors for the shape parameters under squared-error loss function (as a symmetric loss function) and zero-one loss functions (as asymmetric loss functions) .The Bayes estimates are compared with their corresponding maximum likelihood estimates based on a Monte Carlo simulation study.