The EOM-CC theory offers a powerful singlereference framework for computing a variety of electronic states: excited states, ionized states, electron-attached states, and so on. The level of correlation treatment can be systematically improved following the hierarchy of CC/EOM-CC approximations (CC2, CCSD, CC3, CCSDT, • • • ), up to the exact limit. A crucially important trait of this framework is its flexibility in the choice of the EOM operators and the reference Slater determinant, which are adapted to provide a balanced treatment of the set of target states. EOM-CC and CC-RSP formalisms produce the same excitation energies, but can differ in their treatment of state and transition properties. The EOM-CC framework allows for the description of properties as generalized expectation values that are obtained by parameterizing exact ex-pressions using eigenenergies and left and right eigenvectors of the (non-Hermitian) similaritytransformed EOM-CC Hamiltonian. EOM-CC response properties within this "expectationvalue approach" have been shown to be identical to the response properties derived from the coupled cluster--configuration interaction (CC-CI) model, where the time-dependent Schrödinger equation is solved using an exponential parametrization to describe the unperturbed system and a linear parametrization to describe the time evolution of the unperturbed system. In CC (and CC-CI) response theory, the expressions for properties are given by derivatives of appropriate (quasi)energy Lagrangians with respect the strength of the external perturbation(s) or, equivalently, from the response of a generalized time-dependent expectation value of a timeindependent one-electron operator. Note that properties computed within the alternative analytic-derivative EOM-CC approach, involving derivatives of (quasi)energy Lagrangians with respect the strength of the external perturbation(s), are identical to those from CC-RSP. CC-RSP requires additional response intermediates for computing multiphoton absorption moments, relative to the EOM-CC expectation-value approach. The EOM-CC expectation-value approach for properties becomes exact in the limit of full configuration interaction. This parameterization ensures that the pole structures of frequencydependent properties are not spoiled by artificial poles, which may negatively impact higherorder excited-state properties computed with the CC-RSP approach. This paper presents a new extension of EOM-CC theory for modeling two-photon absorption (2PA) cross sections in the X-ray regime (X2PA). This development is motivated by the need for robust high-level first-principles tools for modeling X2PA processes, which occur in experiments involving intense X-ray radiation sources such as X-ray free-electron lasers (XFEL). Similarly to the UV-vis domain, X2PA has different selection rules than one-photon X-ray absorption (XAS) and could, therefore, deliver complementary information.