The MP2/6-31G*// HF/6-31G*. B3LYP/6-31G* level studies on NH4+ (H2O)(20) suggest that the cluster with a NH4+ ion in the dodecahedral cavity (isomer 1)has almost the same energy as the cluster with a NH4+ ion on the cage surface and a neutral water molecule in the cavity (isomer 2). The NH3(H2O)(20)H+ cluster (isomer 3) with a neutral NH3 molecule in the cavity and a hydronium ion on the surface is significantly less stable. These results are sharply different from those of (H2O)(21)H+ isomers in which hydronium ion is always on the cage surface [Chem. Phys. Lett. 319 (2000) 440] and a neutral water molecule in the cavity.