We present GALEX near-ultraviolet (NUV: 1750-2750 Å) and far-ultraviolet (FUV: 1350-1750 Å) imaging observations of two 1.2° diameter fields in the Hyades and Pleiades open clusters in order to detect possible UV variability of the member stars. We have performed a detailed software search for short-term UV flux variability during these observations of the ∼400 sources detected in each of the Hyades and Pleiades fields to identify flarelike (dMe) stellar objects. This search resulted in the detection of 16 UV variable sources, of which 13 can be directly associated with probable M-type stars. The other UV sources are G-type stars and one newly discovered RR Lyrae star, USNOB1.0 1069-0046050, of period 0.624 day and distance ∼4.5 to 7 kpc. Light curves of photon flux versus time are shown for seven flare events recorded on six probable dMe stars. UV energies for these flares span the range 2 × 1027 to 5 × 1029 erg, with a corresponding variability change of ΔNUV = 1.82 mag. Only one of these flare events (on the star Cl* Melotte 25 LH129) can definitely be associated with an origin on a member of the Hyades cluster itself. Finally, many of our M-type candidates show long periods of enhanced UV activity but without the associated rapid increase in flux that is normally associated with a flare event. However, the total UV energy output during such periods of increased activity is greater than that of many short-term UV flares. These intervals of enhanced low-level UV activity concur with the idea that, even in quiescence, the UV emission from dMe stars may be related to a superposition of many small flare events possessing a wide range of energies.