The binding energy of the exciton in the symmetric and asymmetric GaAs/Ga1-xAlxAs quantum wells is calculated with the use of a variational approach. Results have been obtained as a function of the potential symmetry, and the size of the quantum well in the presence of an arbitrary magnetic field. The applied magnetic field is taken to be parallel to the axis of growth of the quantum well structure. The role of the asymmetric barriers, mag netic field, and well width in the excitonic binding is discussed as the tunability parameters of the GaAs/Ga1-xAlxAs system. (C) 1998 Academic Press.