In　this　paper,　we　use　the　notion　of　log　likelihood　ratio　to　obtain　the　limit　properties　of　the　sequences　of　dependent　nonnegative　integrable　random　variables.　A　kind　of　strong　limit　theorem　represented　by　inequalities　which　we　call　the　strong　deviation　theorem　is　obtained.　The　bounds　given　by　these　theorems　depend　on　sample　point.　Crown　Copyright　(c)　2008　Published　by　Elsevier　B.V.　All　rights　reserved.