A theoretical study of the magnetization curves of quasiperiodic magnetic multilayers is presented. We consider structures composed by ferromagnetic films (Fe) with interfilm exchange coupling provided by intervening nonferromagnetic layers (Cr). The theory is based on a realistic phenomenological model, which includes the following contributions to the free magnetic energy: Zeeman, cubic anisotropy, bilinear and biquadratic exchange energies. The experimental parameters used here are based on experimental data recently reported, which contain sufficiently strong biquadratic exchange coupling.