Abstract <p>Moments of a distribution are useful in studying its useful properties. The relations for moments of generalized and dual generalized order statistics are useful to obtain higher order moments from some lower order moments. In this paper, some recurrence relations are obtained for the moments of generalized and dual generalized order statistics for a transmuted family of distributions. Some characterizations are also obtained for the transmuted family of distributions in terms of single and joint moments of generalized and dual generalized order statistics. Some examples are also given.</p>