Abstract: Ultrathin ferromagnetic biaxial films exhibit uniaxial anisotropy induced by underlayer and double shifted magnetization curves. Two possible origins of the double shifted curves are identified from experimental data, namely, the step-induced anisotropy and the exchange-coupled induced interfacial anisotropy. Micromagnetic study of modified astroids with starlike shapes indicates that a large uniaxial anisotropy induced by the interface plays a key role in the formation of double shifted magnetization waves. An additional bias field along the easy axis may enhance the shifted field. The present research status, both experimental and theoretical, is briefly discussed.