1. A PROCESS FOR PRODUCING A FLAME-RETARDANT POLYMER WHICH COMPRISES WARMING A MIXTURE OF (1) AN AZIRIDINYL COMPOUND SELECTED FROM THE GROUP CONSISTING OF A 1-AZIRIDINYL PHOSPHINE OXIDE AND A 1-AZIRIDINYL PHOSPHINE SULFIDE WITH (2) A METHYLOL PHOSPHORUS COMPOUND SELECTED FROM THE GROUP CONSISTING OF TRIS (HYDROXYMETHYL) PHOSPHINE OXIDE, TETRAKIS (HYDROXYMETHYL) PHOSPHONIUM CHLORIDE, AND A REACTION PRODUCT OF SAID METHYLOL, PHOSPHORUS COMPOUND WITH A COMPOUND CONTAINING AT LEAST ONE TRIVALENT NITROGEN, ATOM AND AT LEAST ONE MEMBER OF THE GROUP CONSISTING OF H-AND-CH2OH ATTACHED TO A TRIVALENT NITROGEN, THE PROPORTIONS OF AZIRIDINYL COMPOUND TO METHYLOL PHOSPHORUS COMPOUND BEING SUCH THAT ONE AZIRIDINYL GROUP IS PRESENT FOR EACH TWO METHYLOL GROUPS OF THE METHYLOL PHOSPHORUS COMPOUND, AND CONTINUING WARMING OF THE MIXTURE UNTIL SAID AZIRIDINYL COMPOUND AND SAID MTHYLOL PHOSPHORUS COMPOUND HAVE REACTED WITH EACH OTHER TO FORM A POLYMERIC REACTION PRODUCT.