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We show that the attractor mechanism for generic black hole is a consequenceof the double-horizon. Investigation of equations of motion shows that in thecase of the double-horizon black holes, the dynamics of the geometry, thescalars and the gauge fields at the horizon decouples from the rest of thespace.  In the general case, the value of the fields at the horizon satisfies anumber of differential equations of functions of the $\theta$ coordinate.  We show this for the case of rotating and non-rotating electrically chargedblack holes in the general two derivative theories of gravity and f(R)gravities including the theories with cosmological constant.Comment: 17 pages, no figures, typos corrected, reference adde

Double-horizon limit and decoupling of the dynamics at the horizon