We prove that one-dimensional asymmetric double-well potentials of deg
ree four have the property that, at a fixed energy, the classical peri
od is the same in both wells. Quantum mechanically this reflects in a
simultaneous occurrence, or alignment, of the spectral quasidegeneraci
es at certain values of the parameters controlling the shape of the po
tential. Experimental applications of this property, like multiresonan
ce tunneling effect, are discussed.