The binding energies for 1S-, 2 P Ϯ -, and 3 P Ϯ -like exciton states and some allowed transition energies between these states have been calculated in GaAsGa 0.7 Al 0.3 As double quantum wells as a function of the well and barrier widths in the presence of a magnetic field applied in the growth direction. We have used the effective-mass approximation and considered the symmetric and asymmetric well widths in the double quantum well structure. We have found that the binding energy of the ground and all exciton excited states is higher in double quantum well structures, when the width of the wells are slightly different ͑asymmetric case͒, than when they are equal ͑symmetric case͒, a diference which is increased by the barrier width. Our results show that the binding energy of the exciton ground state increases with the magnetic field for all values of the well widths. We have found that the binding energy of the 2 P ϩ -and 3 P Ϯ -like excitonic states decreases with the magnetic field, which additionally splits the binding energies of the nP (mϭϮ1) excited states. This behavior is similar to that observed in single quantum wells.