A series of MkF2k-1+ (M = Mg, Ca; k = 2, 3) cations have been theoretically investigated to make a new attempt to design superalkali species. As expected, most of these cations were identified as pseudoalkali or even superalkali cations in view of their low electron affinities (EAs). The stability of these cationic clusters is indicated by considerable HOMO-LUMO gaps and positive dissociation energies. More intriguingly, these alkaline-earth-metal-based cations have advantages over alkali-metal-based superalkalis in two aspects: (1) they possess much larger binding energy values; (2) they can keep the chemical stability along with the increasing cluster size. Therefore, it is proposed here that the alkaline-earth-metal atoms could partner with halogens to construct stable cations of low EA value, which may add new candidates to the superalkali family.