The present invention relates to heterocyclo alkylsulfonyl pyrazoles of the formula I: ##STR00001## wherein the ring of the formula (R.sup.5)--A--(SO.sub.mR.sup.4), m, X, R.sup.1 through R.sup.5 are as defined in the specification, to pharmaceutical compositions containing them and to their medicinal use. The compounds of the invention are useful in the treatment or alleviation of inflammation and other inflammation associated disorders, such as arthritis, colon cancer, and Alzheimer's disease in mammals, preferably humans, dogs, cats and livestock animals.