Optical flares on early F- and A-type stars have never been observed with certainty. Inspection of several thousands of these stars in the Kepler public archives resulted in the discovery of flares in 25 G-type and 27 F-type stars. Because A-type stars are thought not to be active, the detection of flares on 19 A-type stars from a sample of nearly 2000 A stars is particularly noteworthy. The flares have relative intensities in the range 1–100 parts per thousand and typical durations of a few minutes to several hours. The mean interval between flares varies between 1 and 120 days. We estimate the typical energy of flares to be around 1035 erg in the F-type stars and about 1036 erg in the A-type stars. Nearly all these stars vary at a low level with a period which is most likely the rotational period of the star. Comparison of the relative flare intensities with those in cool red stars observed by Kepler shows that flares in these stars, and certainly in the A-type stars, cannot easily be ascribed to cool flare-star companions. The huge energy released in the flares is difficult to understand. This is especially the case for A-type stars since these stars are thought to have very weak magnetic fields. The flare energy may possibly originate in magnetic reconnection of field lines between the primary star and a companion.