Polyhydrazides and poly(amide-hydrazide)s were prepared from two ethersulfone-dicarboxylic acids, 4,4 '-[sulfonylbis(1,4-phenylene)dioxy]dibenzoic acid and 4,4 '-[sulfonylbis(2,6-dimethyl-1,4-phenylene)dioxy] dibenzoic acid, or their diacyl chlorides with terephthalic dihydrazide, isophthalic dihydrazide, and p-aminobenzhydrazide via a phosphorylation reaction or a low-temperature solution polycondensation. All the hydrazide polymers were found to be amorphous according to X-ray diffraction analysis. They were readily soluble in polar organic solvents such as N-methyl-2-pyrrolidone and N,N-dimethylacetamide and could afford colorless, flexible, and tough films with good mechanical strengths via solvent casting. These hydrazide polymers exhibited glass-transition temperatures of 149-207 degreesC and could be thermally cyclodehydrated into the corresponding oxadiazole polymers in the solid state at elevated temperatures. Although the oxadiazole polymers showed a significantly decreased solubility with respect to their hydrazide prepolymers, some oxadiazole polymers were still organosoluble. The thermally converted oxadiazole polymers had glass-transition temperatures of 217-255 degreesC and softening temperatures of 215-268 degreesC and did not show significant weight loss before 400 degreesC in nitrogen or air. For a comparative study, related sulfonyl polymers without the ether groups were also synthesized from 4,4 ' -sulfonyldibenzoic acid and the hydrazide monomers by the same synthetic routes.