In sect. Ceratophora Dahist. T. krättlii (Piz Padella) is described. In sect. Alpina Hagl. a number of new sp. are described, a few only restricted to the western+ or to the eastern++ Alps: T. carinthiacum (also western Balcans), T. helveticum (also Tatra) with f. lobatum, T. mattmarkense+, T. panalpinum (also high mountains in Spain, Tatra and Transsilvanian Alps, western Balcans), T. parsennense -++, T. pseudofontanum, T. saasense +, T. vereinense, T. vernelense ++, T. vetteri. The latin description of 2 already known sp. is enlarged: T. apenninum (Tenore) DC. em v.S. (Apennines) and T. petiolulatum 11 (Hüter) v.S. nov. comb.; furthermore T. oreophilum Hagl. and T. venustum Dahlst.++ are treated. In sect. ~ ~ Fontana nov. sect., next to T. fontanum H.M. sens, str., a number of new species are described: T. aurantellum I++ T. corsicum (Corse), T. fontanicolum ++ (also Tatra), T. fonlanosquameum ++, T. peralatum ++, T. pohlii ++, T. pseudoboreigenum (Central Alps). In connection with this section T. aestivum -2++ and T. crocellum ++ are described. In sect. Cucullata nov. sect., besides T. cucullatum Dahist. and T. tiroliense Dahist., T. fontaniforme (Bernina) is described. In connection with sect. Rhodocarpa v.S. (T. schroeterianum H.M.), T. rufocarpum is described (Alps, W. Balcans). In sect. Vulgaria Dahist. the following sp. are described: T. aequilobiforme 9+^ T. callosum !+, T. complicatum !+ (also Bernina), T. perfissum ++, T. praeticum, T. reophilum, T. rhaeticum, T. serpentinum (central Alps). Photographs of the type specimens of most of the new sp. are published.