Zinc finger genes in mammalian genomes are frequently found to occur in clusters with cluster members appearing in a tandem array on the chromosome. It has been suggested that in situ gene duplication events are primarily responsible for the evolution of such clusters. The problem of inferring the series of duplication events responsible for producing clustered families is different from the standard phylogeny problem. In this paper, we study this inference problem using a graph called duplication model that captures the series of duplication events while taking into account the observed order of the genes on the chromosome. We provide algorithms to reconstruct a duplication model for a given data set. We use our method to hypothesize the series of duplication events that may have produced the ZNF45 family that appears on human chromosome 19.