The internal transitions and absorption spectra of confined magnetoexcitons in GaAs/Ga0.7Al0.3As quantum wells have been theoretically investigated under magnetic fields along the growth direction of the semiconductor heterostructure. The magnetoexciton states are obtained within the effective-mass approximation by using a variational procedure. The trial exciton-envelope wavefunctions are described as hydrogeniclike polynomial functions. The internal transition energies are investigated by studying the allowed magnetoexcitonic transitions using terahertz radiation circularly polarized in the plane of the quantum well. The intraexcitonic magnetoabsorption coefficients are obtained for transitions from 1s-like to 2p^{+-}-like magnetoexciton states as functions of the applied magnetic field.