  Effective field theory (EFT) is generalized to investigate the rotational
motion of triaxially deformed even-even nuclei. A Hamiltonian, called the
triaxial rotor model (TRM), is obtained up to next-to-leading order (NLO)
within the EFT formalism. Its applicability is examined by comparing with a
five-dimensional collective Hamiltonian (5DCH) for the description of the
energy spectra of the ground state and $\gamma$ band in Ru isotopes. It is
found that by taking into account the NLO corrections, the ground state band in
the whole spin region and the $\gamma$ band in the low spin region are well
described. The results presented here indicate that it should be possible to
further generalize the EFT to triaxial nuclei with odd mass number.
