Two-component relativistic equation-of-motion coupled-cluster methods are developed and implemented. Scalar-relativistic and spin–orbit effects are taken into account through a two-component scheme in both Hartree–Fock and correlation calculations. Excitation energies and spin–orbit splittings of atoms and diatomic molecules, and ionization potentials of OsO4 are reported. The advantage of the present two-component scheme is illustrated particularly for heavy-element systems.