High resolution spectrophotometry of the black hole system V404 Cyg during quiescence, performed during 1990 and 1991, is discussed. In addition to a 6.5d orbital modulation, there is strong evidence of a 0.24d periodicity in both the H alpha emission radial velocities and the continuum flux. The relative phasing between the photometric and spectroscopic 0.24d modulations is somewhat puzzling and several interpretations are discussed. Some hints of ellipsoidal modulation in the 6.5d period are also presented.