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We propose three new methods for the definition of derivation rules in O-O conceptual modeling languages. The first method applies to static rules, and associates each derived element with a defining operation. The specification of this operation is then the definition of the corresponding derivation rule. The second method applies to constant relationship types whose instances can be derived when the instances of one of its participant entity types are created. We propose a variant of the previous method to deal with these types. The third method deals with hybrid types, and suggests a simple way to define their partial derivation rules. We propose an adaptation of the three methods to the UML.