Observations of the Pleiades cluster by the method of stellar tracks, carried out on the 40-inch Schmidt telescope of Byurakan Astrophysical Observatory, have resulted in the detection of 49 flares from 38 stars, 17 of which were not previously known to be flare stars. It is shown that for bright stars (U ≤ 16.0) the detection of flares in observations by the method of stellar tracks is at least three times more efficient than for observations by the method of stellar chains. Another advantage of the first method is that one can detect brief flares that last less than 6 min. The visual stellar magnitude at the minimum for the brightest of the flare stars that we found is 11.92. This raised the upper luminosity limit of known flare stars in the Pleiades by 0.21 magnitude. A comparison of the expected number of bright flare stars in the Pleiades with the number of all bright members of the cluster (falling in the range from V ≈ 12.0 to V ≈ 16.0) suggested that all these stars evidently must be flare stars. © 1999 Kluwer Academic/Plenum Publishers.