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 2 H NMR spectroscopy and optical microscopy with polarized light. Two nematic biaxial phases were observed in a very narrow region between the two uniaxial nematic mesophases. The sequence of phase changes, hexagonal-calamitic N C-biaxial NBX + -biaxial NBX --discotic ND-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 NC and NBX + and the NBX --ND mesophases are second order. The order parameters of the ionic headgroup of the surfactant, determined from the 2 H quadrupolar splittings, indicate that the average micelle size decreases with the decanol content in the NC and NBX + mesophases and increases with the decanol content in the NBXand ND mesophases.