A theoretical study of the internal transitions of confined magnetoexcitons in GaAs-Ga1-xAlxAs quantum wells is presented, with the magnetic field applied along the growth direction of the semiconductor heterostructure. The various exciton-envelope wavefunctions are described as products of electron and hole solutions of the associated quantum-well potentials and symmetry-adapted Gaussian functions. The magnetoexciton states are simultaneously obtained by diagonalizing the appropriate Hamiltonian in the effective-mass approximation. Exciton internal transitions are theoretically investigated by studying the allowed magnetoexcitonic transitions using far-infrared (terahertz) radiation circularly polarized in the plane of the quantum well. Theoretical results are obtained for both the intramagnetoexciton transition energies and oscillator strengths associated with excitations from 1s-like to 2s-, 2p(+/-)-, and 3p+/--like magnetoexciton states, and from 2p_- to 2s-like exciton states. The present results are compared with previous theoretical work and available optically detected resonance measurements.14510211033