Several　rapidly　convergent　series　for　the　highly　efficient　calculation　of　the　interaction　energies　between　dissimilar　double　layers　for　CaCl2　type　electrolytes　at　y(0)　＞　y(d)　＞　0　were　derived.　The　accurate　numeral　results　were　given　and　several　approximate　expressions　were　obtained　for　y(0)　＜＜　1.　The　number　of　the　series　terms　required　to　obtain　the　interaction　energies　with　six　significant　digits　is　not　more　than　3　when　the　dimensionless　surface　potential　of　double　layers　y(0)　＜=　20.　The　interaction　energies　between　dissimilar　double　layers　for　Na2SO4　or　CaCl2　type　electrolytes　depend　significantly　on　the　y(d)　value,　while　the　interaction　energies　for　Na2SO4　type　electrolytes　is　practically　independent　of　y　(0).　The　present　results　can　also　be　applied　to　Na2SO4　type　electrolytes　at　y(0)　＜　y(d)　＜　0.