  In this paper we examine gravitational radiation in higher order non-local
gravity described by the non-local gravitational Lagrangian density
$\mathcal{L}_{g}=R+\sum_{h=1}^{n}a_{h}R\Box^{-h}R$. This non-local theory of
gravitation always exhibits the tensor transverse gravitational radiation for
$k_{1}^{2}=0$, corresponding to the angular frequency $\omega_{1}$, composed of
two standard $(+)$ and $(\times)$ polarization modes, massless and of helicity
2. Furthermore, it shows, under suitable constraint and $n\geq 2$, an
additional massive transverse scalar gravitational radiation with helicity 0.
It is composed of $n-1$ modes associated to $n-1$ angular frequencies
$\omega_{2},\ldots,\omega_{n}$, each of which of breathing polarization $(b)$
to lowest order in $\gamma$, a parameter that takes into account the difference
in speed between the slightly massive wave and the massless one. Thanks to NP
formalism, we find that the $E(2)$ class of non-local gravitational waves is
$N_{3}$, according Petrov classification, where the presence or absence of all
modes are observer independent. Also, the scalar radiation is forbidden for
$n=1$ and $n=2$ cases, when some conditions are satisfied. Finally, in
$\Box^{-1}$ gravity where $n=1$, a possible degenerate case with a continuous
infinity of transverse massive scalar breathing modes appears under a
particular constraint, which reproduces in two-dimensional spacetime the
Polyakov effective action.
