In　this　article,　we　propose　a　general　additive-multiplicative　rates　model　for　recurrent　event　data.　The　proposed　model　includes　the　additive　rates　and　multiplicative　rates　models　as　special　cases.　For　the　inference　on　the　model　parameters,　estimating　equation　approaches　are　developed,　and　asymptotic　properties　of　the　proposed　estimators　are　established　through　modern　empirical　process　theory.　In　addition,　an　illustration　with　multiple-infection　data,　from　a　clinic　study　on　chronic　granulomatous　disease　is　provided.