Theoretical calculations supported by numerical simulations show that utilization of the nonlinear dependence of the index of refraction on intensity makes possible the transmission of picosecond optical pulses without distortion in dielectric fiber waveguides with group velocity dispersion. In the case of anomalous dispersion (∂2&ohgr;/∂k2>0) discussed here [the case of normal dispersion (∂2&ohgr;/∂k2<0) will be discussed in a succeeding letter], the stationary pulse is a ``bright'' pulse, or envelope soliton. For a typical glass fiber guide, the balancing power required to produce a stationary 1‐ps pulse is approximately 1 W. Numerical simulations show that above a certain threshold power level such pulses are stable under the influence of small perturbations, large perturbations, white noise, or absorption.