System of succession in a monarchy where females can be heirs to the throne only if there is no male offspring to the current monarch (regardless of age and who was born first). If females can be heirs only when the current monarch has no (applicable) male relatives at all it's called agnatic-cognatic succession (used in the Netherlands, for example). When the firstborn child is heir apparent regardless of gender it's called cognatic succession, this is the case in for example Sweden.

Agnatic succession is used in for example England and Denmark (which both currently have Queens for monarchs, ironically enough).