The Netherlands are a monarchy since 1813/1815 but the same dynasty was already a monarchy de facto since 1585 when a son of Willem I of Nassau, Prince of Orange ('The Silent') succeeded him as Stadtholder (Maurits, and then subsequently followed by Frederik Hendrik, Willem II, Willem III, etc.)
In 1674 the Lords States-General declared the office of Stadtholder hereditary for Willem III of Nassau, Prince of Orange (and King of England, Scotland and Ireland) and for his male descandants. So since then it was a monarchy de jure. The Stadtholder however died without issue.
In 1747 the Lords States-General declared the office of Stadtholder hereditary for both the male and the female issue of Johan Willem Friso of Nassau-Dietz, Prince of Orange. So since then it was a monarchy de jure again. Today's royal family directly stems from this Prince.
As a monarchy means a system in which the highest function of State is delivered by hereditary succession, we can say that the Netherlands, despite the disguising name "Republic" has been a monarchy for the longest time.