The variational procedure, in the effective-mass and parabolic-band approximations, is used in order to investigate the effects of crossed electric and magnetic fields on the exciton states in GaAs/Ga1-xAlxAs coupled double quantum wells. Calculations are performed for double quantum wells under applied magnetic fields parallel to the layers and electric fields in the growth direction. The exciton envelope wave function is obtained through a variational procedure using a hydrogenic 1s-like wave function and an expansion in a complete set of trigonometric functions for the electron and hole wave functions. We take into account intersubband mixing brought about by the Coulomb interaction of electron-hole pairs in double quantum wells and present a detailed analysis of the properties of direct and indirect exciton states in these systems. The present study clearly reveals anticrossing effects on the dispersion with applied voltage (or growth-direction electric field) of the photoluminescence peaks associated with direct and indirect excitons. Calculated results are found in good agreement with available experimental measurements on the photoluminescence peak position associated with direct and indirect excitons in GaAs-Ga1-xAlxAs double quantum wells under growth-direction applied electric fields or under applied in-plane magnetic fields.767