  In the context of the two-body problem in General Relativity, hereditary
terms in the long range gravitational field depend on the history rather than
the instantaneous state of the source at retarded time. We compute the next-to
leading effects of such hereditary terms, that comprise tail and memory, on the
two-body dynamics, within effective field theory methods, including both
dissipative and conservative effects. The former confirm known results at 2.5
post-Newtonian order with respect to the leading order in the luminosity
function; the conservative part is a new result and is an unavoidable
ingredient for a derivation of the conservative two-body dynamics at fifth
post-Newtonian order.
