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Balanced n-ary designs were introduced as a generalization of balanced incomplete block design. Methods of construction of balanced n-ary designs have been developed by many authors. Nested balanced incomplete block designs were introduced for statistical situations where there are two source of variability and one source is nested within the other. In this paper, a method of construction of nested balanced n-ary designs(n 3) and some property has been studied with some examples. The nested balanced n-ary designs thus obtained are shown to satisfy balancedness and nestedness. Nested balanced incomplete designs are a special case of the design considered in this paper.