Uniqueness cnterla of the steady state m porous catalysts are derived by usmg the contractlon mapping prmciple with different norms Among the norms consldered. the one mvolvmg the gradlent of the steady state yields the stromzest result The cntena developed m the present study bear some resemblance to those developed by other methods-The uniqueness of the steady state in porous catalyst particles 1s of much concern m the design of chemical reactors since multiple solutions may cause severe stability problems[l, 21 In a previous paper[31, some uniqueness criteria of the steady state have been developed by means of the contractron mappmg prmciple (hereafter CMP) [4] and Hammerstem's theorem [5] The results are relatively more conservative than those derived from other methods[6,7] It IS conceivable that more liberal results can be obtamed from the CMP If the norm of the function space IS sultably chosen The purpose of this work IS to show how this can be realized m some cases, as well as to demonstrate the way m which the criteria derived via the CMP route are affected by varymg the norm of the function space The results wdl supplement the exlstmg literature on the subject DEVELOPMENT OF A FAMILY OF UNIQUJSNJISS CRITERlA