This　paper　is　devoted　to　build　the　existence-and-uniqueness　theorem　of　solutions　to　stochastic　functional　differential　equations　with　infinite　delay　(short　for　ISFDEs)　at　phase　space　BC((-infinity,　0];　R-d).　Under　the　uniform　Lipschitz　condition,　the　linear　growth　condition　is　weaked　to　obtain　the　moment　estimate　of　the　solution　for　ISFDEs.　Furthermore,　the　existence-and-uniqueness　theorem　of　the　solution　for　ISFDEs　is　derived,　and　the　estimate　for　the　error　between　approximate　solution　and　accurate　solution　is　given.　On　the　other　hand,　under　the　linear　growth　condition,　the　uniform　Lipschitz　condition　is　replaced　by　the　local　Lipschitz　condition,　the　existence-and-uniqueness　theorem　is　also　valid　for　ISFDEs　on　[t(0),　T].　Moreover,　the　existence-and-uniqueness　theorem　still　holds　on　interval　[t(0),　infinity),　where　t(0)　is　an　element　of　R　is　an　arbitrary　real　number.　(C)　2006　Elsevier　Inc.　All　rights　reserved.