propylene copolymer and their derivatives a compatibilizer precursor is used for modifying the polyamide and polyolefin of an amino hydroxyl or epoxy group containing chemical and then a reactive dye and or an acid dye is used for dyeing the polyamide and polyolefin so that the dyed polyamide and polyolefin have excellent dye fastness light fastness rubbing fastness washing fastness and low temperature dyeability to overcome the shortcomings of conventional nylon fibers including a poor dyeing effect a non level dyeing quality a high dyeing temperature and a high cost application_number US 55055809 A description to make it easier for our examiner to understand the technical characteristics and operating procedure of the present invention we use preferred embodiments together with the attached drawings for the detailed description of the invention as follows in a deep dyeing process of polyamide and polyolefin in accordance with the present invention a compatibilizer precursor such as a carboxyl polymer an anhydride polymer a hydroxyl polymer an epoxy polymer and a cyanate based compound and an amino group wherein the amino group containing chemical is one selected from the collection of ethylene diamine diethylenetriamine triethylenetetramine tetra ethylene pentamine pentaethylenehexamine hexaethyleneheptamine polyethylene polyamine and their related derivatives and a hydroxyl group or epoxy group containing chemical are used for modifying the polyamide pa or nylon and polyolefin po and then a reactive dye and or an acid.