The 2-D trajectories ω(x, z, t) of suspended sediment particles result from the combination of two random 1-D chronologic and interdependent displacements series in i = 1, 3 senses, intercalated with periods of time when the grain does not move in these senses. The objectives of the paper are: (i) to restate successful 1-D works carried out in natural streams; (ii) to show that the Random Processes describe the 2-D movements − longitudinal and vertical − of sediment and pollutants in open channel flows; (iii) to present these 2-D Poissonian models; (iv) highlight the importance of temporal and spatial Intensity Mobility Functions in the definition, calibration and validation of random models; and (v) to show how to consider the grain sizes, to describe their behavior in suspension. Temporal and spatial mobility functions, obtained with grains of sediment labeled with radiotracers, permitted to adjust and validate the random models.