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The readback signal of a thin film head from a double-layer perpendicular medium shows enhanced undulations in the amplitude versus density plot. These undulations are an order of magnitude greater than that observed in the longitudinal recording. In addition, the null response usually occurs at a wavelength much longer than the gap length. This anomalous wavelength response is attributed to the interaction between the head and the underlayer. Three models with different degrees of head-underlayer interaction are used to analyze this phenomenon. Experimental data are presented and compared with these models. The effect of the pole length, gap length, medium thickness, and head-to-medium spacing on the wavelength response is also discussed.