We have made a systematic study of the temperature- and field-dependen
ce of the quantum oscillations in the magnetoresistance of the quasi-2
D systems (BEDT-TTF)(2)MHg(SCN)(4) (M=K, Rb, Tl, NH4) and the quasi-1D
system (TMTSF)(2)ClO4 at fields up to 51 T and temperatures down to 3
00 mK. Recent theoretical work can explain the high magnetic-field ind
uced phase transitions observed in these systems.