Methanesulfonamides are structurally depicted by Formula I' ##STR1## or its pharmacologically acceptable salts where R.sub.3 is a C.sub.1-7 alkyl substituted with C.sub.3-7 cycloalkyl, or a C.sub.1-10 alkyl substituted with one to eight fluorine atoms, one to three hydroxy, one to three C.sub.1-5 acyloxy or one to three C.sub.1-4 alkoxy substituents. These compounds are useful as Class III antiarrhythmic agents and are stable against rapid metabolism. Methods for treating cardiac arrhythmias with the compounds of Formula I' as well as compositions thereof are also described.