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In this paper, the transmission of the time and/or frequency signals (e.g., 1 pulse per second and 10 MHz) coded on the optical carrier by means of an on-off intensity modulation in the two-way fiber-optic link is considered. It is assumed that the bidirectional optical amplification in the single piece of an erbium-doped fiber is exploited to compensate the attenuation of the optical path. Such configuration of the amplifiers, offering the highest possible symmetry of the propagation conditions in both directions, is well suited for the two-way transfer method exploiting the symmetry of the link. We proposed the method of estimating interfering signals and jitter, which appear at both sides of such bidirectional fiber link because of Rayleigh backscattering and amplified spontaneous emission. This method is further exploited for finding the gains of bidirectional amplifiers, allowing optimization of the performance of the link. The experiments done with 120- and 220-km-long links, incorporating one and three amplifiers, respectively, confirmed theoretical predictions and proved that the single-path bidirectional amplifiers without any components separating the directions are useful for time or RF frequency transfer. During the experiments, both field-deployed telecommunication cables and the fibers spooled in the laboratory were used. Presented methods of analysis and optimization are useful for designing and evaluating the fiber-optic links incorporating single-path bidirectional fiber-optic amplifiers and exploiting intensity modulation for time and/or frequency transfer.