The concept of generalized order statistics (gos) was introduced by Kamps (1995). Since generalized order statistics is an unified approach of other ordered random scheme, therefore, recurrence relations between moments of generalized order statistics is of special interest. In this paper some recurrence relations for moments of generalized order statistics from doubly truncated Makeham distribution are obtained. Further, the results are deduced for order statistics and record values. In the last section a characterization theorem is presented.