  We study the long-wavelength collective modes in the magnetic-field-induced
spin-density-wave (FISDW) phases experimentally observed in organic conductors
of the Bechgaard salts family, focusing on phases that exhibit a sign reversal
of the quantum Hall effect (Ribault anomaly). We have recently proposed that
two SDW's coexist in the Ribault phase, as a result of Umklapp processes. When
the latter are strong enough, the two SDW's become circularly polarized
(helicoidal SDW's). In this paper, we study the collective modes which result
from the presence of two SDW's. We find two Goldstone modes, an out-of-phase
sliding mode and an in-phase spin-wave mode, and two gapped modes. The sliding
Goldstone mode carries only a fraction of the total optical spectral weight,
which is determined by the ratio of the amplitude of the two SDW's. In the
helicoidal phase, all the spectral weight is pushed up above the SDW gap. We
also point out similarities with phase modes in two-band or bilayer
superconductors. We expect our conclusions to hold for generic two-SDW systems.
