In the potential areas in which the wave characteristics of an optical eigenmode guided in the optical fiber plays an important role, it is substantially required to have the state of polarization (SOP) of the propagating mode stabilized. The birefringence induced externally in the fiber causes a change in the SOP and impairs the function of fiber-optic systems, such as coherent optical communications and interferometric sensors. To overcome this undesirable problem, there have been developed birefringent single-mode fibers capable of maintaining the SOP of the guided mode. Such a fiber has been fabricated to have a highly anisotropic residual stress in the direction of its cross-section in order that a particulary high birefringence is induced in the propagation direction of light. Nevertheless, the SOP can no longer be preserved in the presence of some external perturbations such as pressure and temperature changes even if any kind of such fibers may be employed. This effect will be a factor of phase and amplitude fluctuations for the propagating modes in the fiber. Since the resulting noise effect would be in a close relation to the ultimate performance limitation in the fiber-optic coherent systems, it is invoked to examine how the birefringent single-mode fiber suffers from such external perturbations. The intent of this paper is to present a correlation processing of the phase and amplitude fluctuations for the orthogonal eigenmodes guided in an externally perturbed birefringent single-mode fiber.