Recently we have proposed using periodically-spaced, phase sensitive optical parametric ampli ers to balance linear loss in a nonlinear ber-optic communication line Opt. Lett. 18, 803 (1993)]. Here we present a detailed analysis of pulse propagation in such a ber line. Our analysis and numerical simulations show that the length scale over which the pulse evolution occurs is signi cantly increased beyond a soliton period. This is because of the attenuation of phase variations across the pulse's prole by the ampli ers. Analytical evidence is presented which indicates that stable pulse evolution occurs on length scales much longer than the soliton period. This is con rmed through extensive numerical simulation, and the region of stable pulse propagation is found. The average evolution of such pulses is governed by a fourthorder nonlinear di usion equation which describes the exponential decay of arbitrary initial pulses onto stable, steady-state, soliton-like pulses.