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Most research work on optimization of nested queries focuses on aggregate subqueries. In this article, we show that existing approaches are not adequate for nonaggregate subqueries, especially for those having multiple subqueries and certain comparison operators. We then propose a new efficient approach, the nested relational approach, based on the nested relational algebra. The nested relational approach treats all subqueries in a uniform manner, being able to deal with nested queries of any type and any level. We report on experimental work that confirms that existing approaches have difficulties dealing with nonaggregate subqueries, and that the nested relational approach offers better performance. We also discuss algebraic optimization rules for further optimizing the nested relational approach and the issue of integrating it into relational database systems.