  The detection of gravitational wave modes and polarizations could constitute
an extremely important signature to discriminate among different theories of
gravity. According to this statement, it is possible to prove that higher-order
non-local gravity has formally the same gravitational spectrum of higher-order
local gravity. In particular, we consider the cases of $f \left( R, \Box R,
\Box^2 R, \cdots, \Box^n R \right) = R + \sum_{i=1}^n \alpha_i R \Box^i R$
gravity, linear with respect to both $R$ and $\Box^i R$ and $ f \left( R, \Box
R \right) = R + \alpha \left(\Box R\right)^2 $ gravity, quadratic with respect
to $\Box R$, where it is demonstrated the graviton amplitude changes if
compared with General Relativity. We also obtain the gravitational spectrum of
higher-order non-local gravity $ f \left( R, \Box^{-1} R, \Box^{-2} R, \cdots,
\Box^{-n} R \right) = R + \sum_{i=1}^n \alpha_i R \Box^{-i} R$. In this case,
we have three state of polarization and $n+3$ oscillation modes. More in
detail, it is possible to derive two transverse tensor $(+)$ and $(\times)$
standard polarization modes of frequency $\omega_{1}$, massless and with
2-helicity; $n+1$ further scalar modes of frequency
$\omega_{2},\dots,\omega_{n+2}$, massive and with 0-helicity, each of which has
the same mixed polarization, partly longitudinal and partly transverse.
