In case of natural watercourses a permanent, gradually varying flow occurs only very rarely. Moreover at those wa*** courses where bed-load has a role, nearly always non-steady flow is the case. Any change in the flow evidently affects the dist*** covered by one step and the lengths of the rest periods between the single steps. For this reason no restriction has been m*** in the model for the density functions characteristic of the distribution of step lengths of a studied particle as of random *** ables, that isthe step lengths are independent of each other and they represent a random variable having not necessarily only type of density function.As it is well-known, Einstein (2) supposed the distances covered by one step to be equal; while Hul and Sayre (15) applied in their model as starting condition the approach that the step lengths of the bed-load are of exponer*** distribution.