We studied, theoretically, the excitonic energy levels and the optical absorption spectra for double quantum wells, both symmetric and asymmetric, in the presence of a homogeneous magnetic field. Within the effective-mass approach, we expanded the excitonic wave function, in an orthogonal basis formed by the products of electron and hole wave functions in growth direction z, and one-particle solutions of the magnetic Hamiltonian in the x-y plane. We applied our method to the case of AlxGa1-xAs, for which we showed how the exciton wave functions vary, and how the basis functions are mixed in a nontrivial way by the effect of the Coulomb potential. By taking into account all the mixing between the elements in our base, we get anticrossings between excited excitonic states (to the best of our knowledge) not reported previously. The behavior in the excitonic energies and wave functions for different wells and barrier geometries is of importance in double quantum well devices.