provided are : an epoxy resin composition for fiber - reinforced composite materials , which has a good balance between storage stability and fast curing properties at high levels ; a prepreg ; and an epoxy resin composition which exhibits excellent mechanical characteristics as a fiber - reinforced composite material . a resin composition which contains an epoxy resin , dicyandiamide , an imidazole compound and an acidic compound , while satisfying the following conditions -: the time until the heat flow rate reaches the peak top after the epoxy resin composition reaches 100 ° c . is 25 minutes or less as measured by a differential scanning calorimeter at an isothermal temperature of 100 ° c . in a nitrogen gas stream . the time until the heat flow rate reaches the peak top after the epoxy resin composition reaches 60 ° c . is 15 hours or more as measured by a differential scanning calorimeter at an isothermal temperature of 60 ° c . in a nitrogen gas stream . the ratio of the number of epoxy groups to the number of imidazole rings in the epoxy resin composition is from 25 to 90 .