James E. Smith (1793)は包膜の特徴を用いて20属を認めた[19]。Swartzはその分類を発展させ、胞子嚢群と包膜の形質により1801年には30属670種を、1806年には38属720種を扱った[19]。この分類体系では人為的な制限があったが、30年近くこれに代わる分類形質は発見されなかった[19]。Desvaux (1827)は胞子嚢群の形質をより詳細に研究し、デンジソウ科 Marsilées、ヒカゲノカズラ科 Lycopodiées、ゼンマイ科 Osmondées、リュウビンタイ科 Marattiées、シダ科 Filicéesの5科79属1666種に分けた[19]。
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