  We study the stability and instability of periodic traveling waves in the
vicinity of the origin in the spectral plane, for equations of Benjamin-
Bona-Mahony (BBM) and regularized Boussinesq types permitting nonlocal
dispersion. We extend recent results for equations of Korteweg-de Vries type
and derive modulational instability indices as functions of the wave number of
the underlying wave. We show that a sufficiently small, periodic traveling wave
of the BBM equation is spectrally unstable to long wavelength perturbations if
the wave number is greater than a critical value and a sufficiently small,
periodic traveling wave of the regularized Boussinesq equation is stable to
square integrable perturbations.
