The need for more and more accurate gravitational wave templates requires
taking into account all possible contributions to the emission of gravitational
radiation from a binary system. Therefore, working within a
multipolar-post-Minkowskian framework to describe the gravitational wave field
in terms of the source multipole moments, the dominant instantaneous effects
should be supplemented by hereditary contributions arising from nonlinear
interactions between the multipoles. The latter effects are referred to as
tails being described in terms of integrals depending on the past history of
the source. We compute higher-order tail (i.e., tail-of-tail and tail-squared)
contributions to both energy and angular momentum fluxes and their averaged
values along hyperboliclike orbits at the leading post-Newtonian approximation,
using harmonic coordinates and working in the Fourier domain. Due to the
increasing level of accuracy recently achieved in the determination of the
scattering angle in a two-body system by several complementary approaches, the
knowledge of these terms will provide useful information to compare results
from different formalisms.