  As a first step in the computation of the orbital phase evolution of spinless
compact binaries including tidal effects up to the next-to-next-to-leading
(NNL) order, we obtain the equations of motion of those systems and the
associated conserved integrals in harmonic coordinates. The internal structure
and finite size effects of the compact objects are described by means of an
effective Fokker-type action. Our results, complete to the NNL order,
correspond to the second-post-Newtonian (2PN) approximation beyond the leading
tidal effect itself, already occurring at the 5PN order. They are parametrized
by three polarizability (or deformability) coefficients describing the mass
quadrupolar, mass octupolar and current quadrupolar deformations of the objects
through tidal interactions. Up to the next-to-leading (NL) order, we recover
previous results in the literature; up to the NNL order for quasi-circular
orbits, we confirm the known tidal effects in the (PN re-expansion of the)
effective-one-body (EOB) Hamiltonian. In a future work, we shall derive the
tidal contributions to the gravitational-wave flux up to the NNL order, which
is the second step required to find the orbital phase evolution.
