The phase diagram of the nematic mesophases present in the tetradecyltrimethylammonuim bromide/n-decanol/water system was determined. Two distinct biaxial nematic mesophases with opposite diamagnetic and optical anisotropies were identified using H-2 NMR spectroscopy and optical microscopy with polarized light. Two nematic biaxial phases were observed in a very narrow region between the two uniaxial nernatic mesophases. The sequence of phase changes, hexagonal-calamitic N-C-biaxial N-BX(+)-biaxial N-BX(-) -discotic N-D-lamellar mesophases, was observed with increasing decanol content. The phase transition between the two biaxial mesophases is first order, while the phase transitions between the N-C and N-BX(+) and the NBX--N-D mesophases are second order. The order parameters of the ionic headgroup of the surfactant, determined from the H-2 quadrupolar splittings, indicate that the average micelle size decreases with the decanol content in the N-C and N-BX(+) mesophases and increases with the decanol content in the N-BX(-) and N-D mesophases.