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.