Abstract: In general,the research on Earth rotational dynamical theory is based on the model of its rotary symmetry,and thetheory obtained a series of conclusions that were coincident with obse rvation.In practice,the earth is an non-rolling-symmetry ellipsoid,so much as is a ellipsoid as a pear.Therefore,thetheoretical researches on triaxial Earth model should have definite meanings.This paper,in the instance of held magnitude of square of the polar motion and ignored lesser magnitude for all parameter in deductive process,presented dynamical equations for thetriaxial fluid-core rotation of the Earth.The resrlts showed that,thethese dynamical equations is linearity and coupling in the precision mentioned above,moreover,obtained four normal frequencies of thetriaxial fluid-core rotation of Earth.At onetime,it was indicated that if held lesser magnitude in the deductive process,then the dynamical equation for fluid core Earth rotation will be a set of complicated nonlinear equation,and there is not analytic resolution for thetriaxial fluid core Earth mode.