We investigate the effect of the weak refractive-index nonlinearity of optical fibers on pulse shape using computer simulations of long-distance transmission. In this study, fiber losses are canceled by periodically spaced optical amplifiers whose spontaneous emission noise is, however, not included in the simulations. Our analysis is confined to normal pulses and does not consider solitons. We reach several conclusions. 1. If wavelength division multiplexing (WDM) of two channels is used in a uniform fiber without dispersion fluctuations, catastrophic build-up of four-wave mixing occurs if one primary channel is located at the zero-dispersion wavelength. 2. If two pulses with different carrier frequencies "collide" in a uniform fiber with no gain or loss discontinuities, their four-wave mixing products reach a peak during complete pulse overlap. But this spurious power dies away as the pulses separate. This is a general property not restricted to solitons. 3. Two-channel WDM transmission of light modulated in amplitude-shift keying (ASK) format appears feasible at 2.5 Gb/s over distances of 7500 km. The two channels should be spaced 2 to 3 nm apart and at least 0.5 nm below the zero-dispersion wavelength, in the region of normal group velocity dispersion.