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We derive the equation of motion for the relativistic compact binaries in thepost-Newtonian approximation taking explicitly their strong internal gravityinto account. For this purpose we adopt the method of the point particle limitwhere the equation of motion is expressed in terms of the surface integrals. Weexamine carefully the behavior of the surface integrals in the derivation. As aresult, we obtain the Einstein-Infeld-Hoffman equation of motion at the firstpost-Newtonian (1PN) order, and a part of the 2PN order which depends on thequadrupole moments and the spins of component stars. Hence, it is found thatthe equation of motion in the post-Newtonian approximation is valid for thecompact binaries by a suitable definition of the mass, spin and quadrupolemoment.Comment: revised version. 27pages, three tables, revtex. Some errors have been  corrected and some explanations have been adde

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Equation of motion for relativistic compact binaries with the strong field point particle limit: Formulation, the first post-Newtonian order, and multipole terms