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We study the nucleon-nucleon interaction up to next-to-next-to-leading orderusing time-ordered perturbation theory in the framework of manifestlyLorentz-invariant chiral effective field theory. We present the two-pionexchange contribution at one-loop level, which is consistent with thecorresponding non-relativistic expressions in the large-nucleon-mass limit.Using the Born series truncated at one-loop order, we calculate the phaseshifts and mixing angles of the partial waves with the angular momentum $l\geq2$. Comparing with the results of non-relativistic formulation, we find animproved description of the phase shifts for some $D$ waves such as the $^3D_3$one. For the other partial waves, both approaches show the globally similarresults.

Nucleon-nucleon scattering up to next-to-next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: peripheral phases