Two-core fibers are investigated experimentally. Low-loss birefringent single-mode two-core fibers, consisting of two cores and a pair of stress-inducing parts built in a cladding, were prepared. A power exchange of the order of a few millimeters occurs as a result of the coupling between the two cores. It was noted that the power-transfer efficiency shows a good wavelength selectivity because the fiber parameters, such as the core radius and refractive-index difference between the core and cladding of the two cores, are not identical. The Stokes beam of stimulated four-photon mixing, generated in a core by compensating for the material dispersion with the modal birefringence between the two orthogonally polarized fundamental modes, exclusively couples to the core, whereas the pump, first-order Raman Stokes, and anti-Stokes waves of the four-photon mixing remain uncoupled. This wavelength-selective coupling will be useful for various applications, such as in couplers in a wavelength-multiplexing optical system and in a fiber-optical amplifier.