A system of taxonomy of the cryptogams, the Smith system was published in:

Smith, G.M. (1938). . Algae and fungi. McGraw-Hill, New York.

Smith, G.M. (1955). . Bryophytes and pteridophytes. 2nd ed. McGraw-Hill, New York.

Division Chlorophyta

Order 1. Volvocales Family 1. Chlamydomonadaceae Family 2. Volvocaceae Order 2. Tetrasporales Order 3. Ulotrichales Family 1. Ulotrichaceae Family 2. Microsporaceae Family 3. Cylindrocapsaceae Family 4. Chaetophoraceae Family 5. Protococcaceae Family 6. Coleochaetaceae Family 7. Trentepohliaceae Order 4. Ulvales Family 1. Ulvaceae Family 2 Schizomeridaceae Order 5. Schizogoniales Family Schizogoniaceae Order 6. Cladophorales Family 1. Cladophoraceae Family 2. Sphaeropleaceae Order 7. Oedogoniales Family Oedogoniaceae Order 8. Zygnematales Family 1. Zygnemataceae Family 2. Mesotaeniaceae Family 3. Desmidiaceae Order 9. Chlorococcales Family 1. Chlorococcaceae Family 2. Endosphaeraceae Family 3. Characiaceae Family 4. Protosiphonaceae Family 5. Hydrodictyaceae Family 6. Oöcystaceae Family 7. Scenedesmaceae Order 10. Siphonales Family 1. Bryopsidaceae Family 2. Caulerpaceae Family 3. Halicystaceae Family 4. Codiaceae Family 5. Derbesiaceae Family 6. Vaucheriaceae Family 7. Phyllosiphonaceae Order 11. Siphonocladiales Family 1. Valoniaceae Family 2. Dasycladaceae

Order Charales Family Characeae

Division Euglenophyta

Order 1. Euglenales Order 2. Colaciales (Euglenocapsales)

Division Pyrrophyta

Order 1. Gymnodiniales Order 2. Peridiniales Order 3. Dinophysidales Order 4. Rhyzodiniales Order 5. Dinocapsales Order 6. Dinotrichales Order 7. Dinococcales

Division Chrysophyta

Order 1. Heterochloridales Order 2. Rhizochloridales Order 3. Heterocapsales Order 4. Heterotrichales Order 5. Heterococcales Order 6. Heterosiphonales

Order 1. Chrysomonadales Suborder 1. Cromulinae Suborder 2. Isochrysidineae Suborder 3. Ochromonadineae Order 2. Rhizochrysidales Order 3. Chrysocapsales Order 4. Chrysotrichales Order 5. Chrysosphaerales

Order 1. Centrales Order 2. Pennales

Division Phaeophyta

  • Class 1. Isogeneratae

Order 1. Ectocarpales Order 2. Sphacelariales Order 3. Tilopteridales Order 4. Cutleriales Order 5. Dictyotales

  • Class 2. Heterogeneratae

Subclass 1. Haplostichineae Order 1. Chordariales Order 2. Sporochnales Order 3. Desmarestiales Subclass 2. Polystichineae Order 1. Punctariales Order 2. Dictyosiphonales Order 3. Laminariales

  • Class 3. Cyclosporeae

Order Fucales

Division Cyanophyta

Order 1. Chroococcales Order 2. Chamaesiphonales Order 3. Hormogonales

Division Rhodophyta

Subclass 1. Bangioideae Order Bangiales Subclass 2. Florideae Order 1. Nemalionales Order 2. Gelidiales Order 3. Cryptonemiales Order 4. Gigartinales Order 5. Rhodymeniales Order 6. Ceramiales

Division Myxothallophyta

  • Class 1. Myxomycetae

Subclass 1. Endosporeae Subclass 2. Exosporeae

Division Eumycetae

  • Class 1. Phycomycetae

Order 1. Chytridiales Family 1. Rhizidiaceae Family 2. Olpidiaceae Family 3. Synchytriaceae Family 4. Cladochytriaceae Family 5. Woroninaceae Order 2. Blastocladiales Order 3. Monoblepharidales Order 4. Ancylistales Order 5. Saprolegniales Family 1. Saprolegniaceae Family 2. Leptomitaceae Family 3. Pythiaceae Order 6. Peronosporales Order 7. Mucorales Order 8. Entomophthorales

Subclass 1. Protoascomycetae Subclass 2. Euascomycetae Order 1. Aspergillales Order 2. Erysiphales Order 3. Hysteriales Order 4. Phacidiales Order 5. Pezizales Order 6. Tuberales Order 7. Helvellales Order 8. Exoascales Order 9. Hypocreales Order 10. Sphaeriales Order 11. Dothidiales Order 12. Laboulbeniales

  • Class 3. Basidiomycetae

Subclass 1. Eubasidii Order 1. Agaricales (Hymenomyceatae) Order 2. Lycoperdales (Gasteromycetae) Order 3. Dacryomycetales Order 4. Tremellales Order 5. Auriculariales Subclass 2. Hemibasidii Order 1. Urediniales Order 2. Ustilaginales Family 1. Ustilaginaceae Family 2. Tilletiaceae

Subclass 1. Ascholichenes Subclass 2. Basidiolichenes

Division Bryophyta

Order 1. Sphaerocarpales Family 1. Sphaerocarpaceae Family 2. Riellaceae Order 2. Marchantiales Family 1. Ricciaceae Family 2. Corsiniaceae Family 3. Targioniaceae Family 4. Monocleaceae Family 5. Marchantiaceae Order 3. Jungermanniales Suborder 1. Metzgerineae Suborder 2. Jungermannineae Order 4. Calobryales

Order 1. Anthocerotales

Subclass 1. Sphagnobrya Subclass 2. Andreaeobrya Subclass 3. Eubrya

Division Psilophyta

  • Class 1. Psilophytinae (psilophytes)

Order 1. Psilophytales Family 1. Rhyniaceae Family 2. Psilophytaceae Family 3. Pseudosporochnaceae Family 4. Zosterophyllaceae Family 5. Asteroxylaceae Order 2. Psilotales

Division Lepidophyta

  • Class 1. Lycopodinae (lycopods)

Order 1. Lycopodiales Family 1. Protolepidodendraceae Family 2. Lycopodiaceae Order 2. Selaginellales Family 1. Selaginellaceae Family 2. Miadesmiaceae Order 3. Lepidodendrales Family 1. Lepidodendraceae Family 2. Lepidocarpaceae Family 3. Bothrodendraceae Family 4. Sigillariaceae Order 4. Isoetales Family 1. Pleuromeiaceae Family 2. Isoetaceae

Division Calamophyta

  • Class 1. Equisetinae (horsetails)

Order 1. Hyeniales Order 2. Sphenophyllales Order 3. Equisetales Family 1. Calamitaceae Family 2. Equisetaceae

Division Pterophyta

Subclass 1. Primofilices (or Inversicatenales, Coenopterideae, Palaeopteridales) Order 1. Protopteridales Family 1. Protopteridaceae Family 2. Cladoxylaceae Order 2. Coenopteridales Family 1. Zygopteridaceae Family 2. Botryopteridaceae Family 3. Anachoropteridaceae Order 3. Archaeopteridales Subclass 2. Eusporangitae Order 1. Ophioglossales Order 2. Marattiales Subclass 3. Leptosporangiatae Order 1. Filicales Family 1. Osmundaceae Family 2. Schizaeaceae Family 3. Gleicheniaceae Family 4. Matoniaceae Family 5. Dipteridaceae Family 6. Hymenophyllaceae Family 7. Cyatheaceae Family 8. Dicksoniaceae Family 9. Polypodiaceae Family 10. Parkeriaceae Order 2. Marsileales Order 3. Salviniales