A system of taxonomy of the cryptogams, the Smith system was published in: Smith, G.M. (1938). Cryptogamic Botany, vol. 1. Algae and fungi. McGraw-Hill, New York. Smith, G.M. (1955). Cryptogamic Botany, vol. 2. Bryophytes and pteridophytes. 2nd ed. McGraw-Hill, New York.
Division Chlorophyta
Class 1. Chlorophyceae
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
Class 2. Charophyceae
Order Charales
Family Characeae
Division Euglenophyta
Order 1. Euglenales
Order 2. Colaciales (Euglenocapsales)
Division Pyrrophyta
Class 1. Cryptophyceae
Class 2. Desmokontae
Class 3. Dinophyceae
Order 1. Gymnodiniales
Order 2. Peridiniales
Order 3. Dinophysidales
Order 4. Rhyzodiniales
Order 5. Dinocapsales
Order 6. Dinotrichales
Order 7. Dinococcales
Division Chrysophyta
Class 1. Xanthophyceae (Heterokontae) Order 1. Heterochloridales Order 2. Rhizochloridales Order 3. Heterocapsales Order 4. Heterotrichales Order 5. Heterococcales Order 6. Heterosiphonales Class 2. Chrysophyceae Order 1. Chrysomonadales Suborder 1. Cromulinae Suborder 2. Isochrysidineae Suborder 3. Ochromonadineae Order 2. Rhizochrysidales Order 3. Chrysocapsales Order 4. Chrysotrichales Order 5. Chrysosphaerales Class 3. Bacillariophyceae 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
Class Myxophyceae (Cyanophyceae) Order 1. Chroococcales Order 2. Chamaesiphonales Order 3. Hormogonales