We　propose　a　scheme　of　generating　multi-component　entangled　coherent　states　of　cavity　fields.　In　this　scheme,　the　atoms　pass　through　cavities　one　by　one,　simultaneously　driven　by　a　strong　classical　field　in　each　cavity.　Then　the　detection　of　the　atomic　states　collapses　the　cavity　fields　onto　multi-component　entangled　coherent　states.　It　is　shown　that,　with　a　judicious　choice　of　the　parameters　of　the　classical　field,　we　can　conditionally　produce　macroscopic　multi-dimensional　maximal　entanglement　for　the　cavity　modes.