Propagation characteristics of pulse waves in rain, fog, and turbulence are determined by a two-frequency mutual coherence function. Parabolic differential equations applicable to strong fluctuation cases are derived for the two-frequency mutual coherence function for randomly distributed scatterers and turbulence. These equations are solved for the plane wave case using the eigenfunction-eigenvalue method. Numerical calculations are given for millimeter waves (100 GHz) and optical waves (0.6943 and 10.6 μm) in rain, fog, and turbulence over the distance of 5 km. The coherence bandwidths are found to be in the range of MHz for millimeter waves (100 GHz) in heavy rain (25 mm/hr) and for optical waves in fog, and considerable distortion of pulse shape may result in these situations. For other cases, the effect on pulse shape distortion may be negligibly small.