A processing composition having a bleaching ability which is used for processing silver halide color photographic materials, and containing a metal chelate compound formed fromthe salt of a metal selected from the group consisting of Fe(III), Mn(III), Co(III), Rh(II), Rh(III), Au(II), Au(III) and Ce(IV), andat least one of a compound represented by formula (I) and a compound represented by formula (II): ##STR1## wherein L.sub.1 and L.sub.2 each represents ##STR2## X.sub.1 and X.sub.2 each represents an oxygen atom or a sulfur atom, R, R.sub.1, R.sub.2 and R.sub.3 each represents a hydrogen atom or an aryl or alkyl group which may be substituted, R.sub.4 represents an aryl or alkyl group which may be substituted, ##STR3## or --OR.sub.7, R.sub.5 and R.sub.6 each has the same meaning as R.sub.1, R.sub.7 represents an aryl or alkyl group which may be substituted, Y.sub.1 and Y.sub.2 each represents an arylene or alkylene group which may be substituted, R, L.sub.1 and L.sub.2 may be joined together to form rings; ##STR4## where X.sub.1, X.sub.2, Y.sub.1, Y.sub.2, R.sub.1, R.sub.2, R.sub.3 and R.sub.4 have the same meaning as in formula (I), R.sub.a, R.sub.b and R.sub.c each represents a hydrogen atom or an aryl or alkyl group which may be substituted, R.sub.a, R.sub.b, R.sub.c and L.sub.3 may be joined together to form rings, and W represents a divalent linking group; or a processing composition having a bleaching ability which is used for processing silver halide color photographic materials, and containing a compound which has a standard electron migration rate constant k.sub.s in a gelatin film of at least 8.times.10.sup.-4 cm/s; anda method for processing silver halide color photographic materials after development with the above processing composition.