  We study the dispersive properties of a linear equation in one spatial
dimension which is inspired by models in peridynamics. The interplay between
nonlocality and dispersion is analyzed in detail through the study of the
asymptotics at low and high frequencies, revealing new features ruling the wave
propagation in continua where nonlocal characteristics must be taken into
account. Global dispersive estimates and existence of conserved functionals are
proved. A comparison between these new effects and the classical local {\it
scenario} is deepened also through a numerical analysis.
