Particle size spectra if foraminifera and diatoms in near-surface ocean water and sediments can generally be represented by a relationship of the type dN/dr=Ar-b. Stokes settling of the particles of density that is uniform and independent of the particle radius r would result in the spectrum slope value of b-2 in the sediment, when b characterizes the parent particle population in the water. For particles the density of which depends on r, such as for thin wall spheres filled with water, the difference between the spectrum slopes is unity, giving b-1 in the sediment. From the data available for this study, the values of b for sediments are on the average smaller by 0.7 than those of the spectrum slope in the settling samples. Dissolution of settling particles produces broad maximums near 3-5 μm in the particle size spectra (dN/dr) owing to the faster dissolution of the smaller particles. We also consider a model of a particle fragmentation that assumes that some fraction of the parent particle population breaks into fragments, and thus a residual population of whole particles is left behind. In this model the residual population of whole particles has the spectrum slope steeper (b+c) than in the parent population (b). The deduced size spectrum of fragments in this model is found to be nonlinear. The similarities and diiferences between this fragmentation model and the Rosin-Weibull distribution law for fragmented materials are discussed in the text.