Several　rapidly　convergent　series　for　highly　efficient　calculation　of　the　interaction　energies　between　dissimilar　double　layers　for　Na2SO4-type　electrolytes　at　y　(0)　＞　y　(d)　＞　0　are　derived,　the　accurate　numerical　results　are　given,　and　several　approximate　expressions　are　obtained　for　y　(0)　＜　1.　The　number　of　the　series　terms　required　to　obtain　the　interaction　energies　with　six　significant　digits　via　the　use　of　the　series　derived　is　no　more　than　2　when　the　dimensionless　surface　potential　of　double　layers　y　(0)　＜=　20.　The　interaction　energies　between　dissimilar　double　layers　for　NaCl-or　Na2SO4-type　electrolytes　are　remarkably　affected　by　the　value　of　y　(d),,　but　the　interaction　energies　for　Na2SO4-type　electrolytes　are　hardly　affected　by　the　value　of　y　(0).　The　present　results　can　also　be　applied　to　CaCl2-type　electrolytes　at　y　(0)　＜　y　(d)　＜　0.