In this paper, we consider the distribution of discounted dividend payments until ruin under a risk model with two independent classes of claims in which both of the two interclaim times have phasetype distributions and a constant dividend barrier. We obtain the integro-dierential equations with boundary conditions for the momentgenerating function of the sum of the discounted dividend payments until ruin. Explicit expressions for arbitrary moments of the discounted dividend payments are

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... if the distribution of the two classes claim amount both belong to the rational family. Finally, numerical illustrations are presented to show how the results are applied.