We present a novel approach to deal with the problem of reconstructing the duplication history of tandemly repeated genes that are supposed to have arisen from unequal recombination. We first describe the mathematical model of evolution by tandem duplication and introduce duplication histories and duplication trees. We then provide a simple recursive algorithm which determines whether or not a given rooted phylogeny can be a duplication history and another algorithm that simulates the unequal recombination process and searches for the best duplication trees according to the maximum parsimony criterion. We use real data sets of human immunoglobulins and T-cell receptors to validate our methods and algorithms. Identity between most parsimonious duplication trees and most parsimonious phylogenies for the same data, combined with the agreement with additional knowledge about the sequences, such as the presence of polymorphisms, shows strong evidence that our reconstruction procedure provides good insights into the duplication histories of these loci.