  In this paper, we generalize the integration rules for scattering equations
to situations where higher-order poles are present. We describe the strategy to
deduce the Feynman rules of higher-order poles from known analytic results of
simple CHY-integrands, and propose the Feynman rules for single double pole and
triple pole as well as duplex-double pole and triplex-double pole structures.
We demonstrate the validation and strength of these rules by ample non-trivial
examples.
